The term plasma antenna has been applied to a wide variety of antenna concepts that incorporate some use of an ionized medium. In the vast majority of approaches, the plasma, or ionized volume, simply replaces a solid conductor. A highly ionized plasma is essentially a good conductor, and therefore plasma filaments can serve as transmission line elements for guiding waves, or antenna surfaces for radiation.
This document discusses various methods for detecting neutrinos. It is very difficult to detect neutrinos due to their weak interactions. The earliest detection was through inverse beta decay using a nuclear reactor. Later, the Sudbury Neutrino Observatory was able to detect neutrinos via different interactions in deuterium, providing evidence of neutrino flavor oscillations. Now, large detectors like IceCube are detecting high-energy neutrinos from astrophysical sources. Measuring the neutrino mass precisely remains challenging but various techniques using beta decay spectra provide upper limits.
This Presentation include
-Introduction to Plasma Physics.
-Plasma: Fourth State of Matter.
-Comparison of Plasma and Gas Phase.
-Fusion Energy
-Future of Plasma Physics.
-Applications.
-Btech Science Fair, RKGIT Ghaziabad
This document summarizes key concepts about laser beams and optical resonators:
1) Laser beam propagation can be described by the Helmholtz equation, with one solution being a Gaussian beam profile. The beam waist radius varies along the beam axis according to the Rayleigh range.
2) Optical resonators provide feedback to turn an amplifier into an oscillator. They contain mirrors between which light bounces and is amplified on each pass through the gain medium.
3) Resonator stability depends on the curvature and separation of the mirrors. Different resonator types support distinct transverse mode patterns within the beam.
The Compton effect occurs when a high-energy photon collides with an electron, causing the photon to lose some energy and increase in wavelength. Arthur Holly Compton discovered this effect in 1923 through experiments bombarding a graphite target with x-rays and measuring the wavelength of scattered radiation. The effect showed that light behaves as both a particle and wave and is important in fields like radiation therapy and gamma spectroscopy. It is explained by the transfer of momentum and energy between the photon and electron during collision.
The document discusses the interaction of radiation with matter. It describes different types of interactions including the photoelectric effect, Compton scattering, and pair production. These interactions vary based on the photon energy and atomic number of the absorbing material. The photoelectric effect is more likely for low energy photons and high atomic number materials. Compton scattering does not depend on atomic number. Pair production requires the highest minimum photon energy and is more likely for high atomic number materials. The document also discusses attenuation coefficients and how they relate to the probability of each interaction type.
Using Metamaterials as Optical Perfect AbsorberSepehr A. Benis
Article review and presentation on basics of using metamaterials as optical perfect absorbers
Metamaterial Course Final Project ( Optional Graduate Course )
Dr. Leyla Yousefi
The term plasma antenna has been applied to a wide variety of antenna concepts that incorporate some use of an ionized medium. In the vast majority of approaches, the plasma, or ionized volume, simply replaces a solid conductor. A highly ionized plasma is essentially a good conductor, and therefore plasma filaments can serve as transmission line elements for guiding waves, or antenna surfaces for radiation.
This document discusses various methods for detecting neutrinos. It is very difficult to detect neutrinos due to their weak interactions. The earliest detection was through inverse beta decay using a nuclear reactor. Later, the Sudbury Neutrino Observatory was able to detect neutrinos via different interactions in deuterium, providing evidence of neutrino flavor oscillations. Now, large detectors like IceCube are detecting high-energy neutrinos from astrophysical sources. Measuring the neutrino mass precisely remains challenging but various techniques using beta decay spectra provide upper limits.
This Presentation include
-Introduction to Plasma Physics.
-Plasma: Fourth State of Matter.
-Comparison of Plasma and Gas Phase.
-Fusion Energy
-Future of Plasma Physics.
-Applications.
-Btech Science Fair, RKGIT Ghaziabad
This document summarizes key concepts about laser beams and optical resonators:
1) Laser beam propagation can be described by the Helmholtz equation, with one solution being a Gaussian beam profile. The beam waist radius varies along the beam axis according to the Rayleigh range.
2) Optical resonators provide feedback to turn an amplifier into an oscillator. They contain mirrors between which light bounces and is amplified on each pass through the gain medium.
3) Resonator stability depends on the curvature and separation of the mirrors. Different resonator types support distinct transverse mode patterns within the beam.
The Compton effect occurs when a high-energy photon collides with an electron, causing the photon to lose some energy and increase in wavelength. Arthur Holly Compton discovered this effect in 1923 through experiments bombarding a graphite target with x-rays and measuring the wavelength of scattered radiation. The effect showed that light behaves as both a particle and wave and is important in fields like radiation therapy and gamma spectroscopy. It is explained by the transfer of momentum and energy between the photon and electron during collision.
The document discusses the interaction of radiation with matter. It describes different types of interactions including the photoelectric effect, Compton scattering, and pair production. These interactions vary based on the photon energy and atomic number of the absorbing material. The photoelectric effect is more likely for low energy photons and high atomic number materials. Compton scattering does not depend on atomic number. Pair production requires the highest minimum photon energy and is more likely for high atomic number materials. The document also discusses attenuation coefficients and how they relate to the probability of each interaction type.
Using Metamaterials as Optical Perfect AbsorberSepehr A. Benis
Article review and presentation on basics of using metamaterials as optical perfect absorbers
Metamaterial Course Final Project ( Optional Graduate Course )
Dr. Leyla Yousefi
Presentation of PhD Thesis: "A perspective on metasurfaces, circuits, holograms and invisibility". Carlo Andrea Gonano, Politecnico di Milano, Italy, 26 January 2016.
This document discusses methods for measuring the velocity of detonation (VOD) of explosives. It describes several point-to-point and continuous methods, including the electric probe method, D'autriche method, resistance wire system, SLIFER system, and TDR system. The electric probe method uses probes placed in the explosive at set distances to measure the time for detonation to travel between them. The D'autriche method calculates VOD based on the proportional VOD of a detonating fuse. Resistance wire and the SLIFER and TDR systems monitor changes in a sensor like a wire or cable as detonation consumes it to determine VOD.
This document discusses key aspects of safely transporting radioactive material as outlined in international regulations. It covers material classification, package selection based on material type and content limits, and controls during transport including limits on radiation levels, transport indexes, and categorizing packages. The overall safety approach involves containing radioactive contents, controlling external radiation, preventing criticality, and preventing heat damage through a graded package design based on material hazard levels.
This document is a project report submitted by Priyanka Verma and Smriti Singh for their Bachelor of Science degree in physics. It discusses elementary particles, including their characteristics, classification, conservation laws, and examples like electrons, positrons, protons, neutrons, pions, and kaons. The report includes certificates of completion from their college principal and physics professors.
Plasma is one of the advanced technology in semi conducting materials. Scientists states that 99% of the universe is covered with plasma. Plasma Antenna is a special type of antenna in which metal conducting elements of conventional antenna are replaced by plasma. Its 4th state of matter similar to gas. It employs ionized gas enclosed in a tube as conducting element of an antenna. When the gas is electrically charged or ionized to plasma, it becomes conductive & allowing radio frequency signals to be transmitted or received. When gas is not ionized, the antenna elements ceases to exit. When voltage is applied to an antenna, electric field is produced which causes current to flow in antenna. Due to current flow, magnetic field is produced. It is more advantageous than other antenna due to ionized gas. It has higher effiency & enhanced bandwidth. The fact that the emitting element is formed over the interval needed for the emission of an electromagnetic pulse is an important advantage of plasma antennas . In the passive state (in the absence of plasma in the discharge tube),such a device does not exhibit electric conductivity. A plasma stream flowing from a jet into the ambient space , the plasma trace of a body moving at an ultrasonic velocity in the atmosphere , and alternative plasma objects have been studied as possible antenna elements.
Metal antennas currently in implementation use metallic conductor as guiding medium for electromagnetic radiations. Plasma antennas uses ionized medium. The plasma antenna is a radiofrequency antenna formed by a plasma columns, filaments or sheets, which are excited by a surface wave. The relevance of this device is how rapidly it can be turned on and off only applying an electrical pulse. Unlike traditional metal antenna, plasma antenna is based on partially or fully ionized gas used as a conducting material
Plasma antennas find its applications in variety of fields due its unique properties, characteristics and advantages over traditional metallic antennas.
i) Faster internet
ii) Public safety networks
iii) Radio and television broadcasting
iv) Space communication
This document provides an overview of plasma physics and its applications. It introduces plasma as the fourth state of matter and discusses its fundamental properties and types. The document outlines various methods for plasma formation, including passive thermal ionization and active generation using external energy sources. Atmospheric and vacuum plasma generation techniques are examined, along with their applications in science, technology, and industry. The document concludes that plasma physics remains an interesting field with opportunities for new discoveries.
DOWNLOAD THE POWERPOINT FILE FROM HERE:
https://www.dropbox.com/s/d8zbqyvc81pgg5w/compton%20effect.pptx?dl=0
Describing Compton Effect from Quantum Mechanics. Presented in East West University.
The document discusses the photoelectric effect and its applications. It begins by explaining Einstein's theory that light consists of quantized packets of energy called photons and how this explains the photoelectric effect. It then discusses how the kinetic energy of emitted electrons increases with higher frequency light. The document also provides a simple diagram of a photoelectric experiment and describes some common applications of the effect, including night vision devices, cameras, and smoke detectors. It ends by showing an image and further explaining how photoelectric smoke detectors work by detecting light scattered by smoke particles.
The document discusses the density of states in two-dimensional systems. It explains that the density of states function describes the number of available energy states in a system and is essential for determining carrier concentrations and distributions. In semiconductors, carrier motion is limited to two, one, or zero spatial dimensions, requiring the density of states to be known in quantum wells (2D), quantum wires (1D), and quantum dots (0D). The document then focuses on the density of states in 2D systems, noting that it is independent of energy and depends on the number of quantized levels in the confined dimension.
There are three main types of laser gain media: gases, liquids, and solids. Gases like CO2 have narrow wavelength gain, while liquids like dyes have broad gain. Solid state lasers like Nd:YAG can have either narrow or broad gain depending on the material. All gain media require pumping to receive energy, which can be optical pumping using lamps or flashlights, or electrical pumping using gas discharges. Q-switching is a technique to produce high power pulses using a Pockels cell to prevent lasing until a population inversion is fully inverted.
Dye lasers use an organic dye dissolved in a liquid as the active lasing medium and can produce a wide range of wavelengths. They work on the principle of population inversion using a pumping source like a flash lamp or other laser to excite the dye molecules. The major components are the active dye medium, pumping source, and resonator mirrors, with one mirror sometimes replaced by a diffraction grating to allow tuning of the output wavelength. Dye lasers offer tunability but have limitations in lifetime and output power.
Explosives, Theory Of Breakage And Blasting Operationspartha sharma
This document discusses explosives and blasting operations. It defines different types of explosives and their ingredients and functions. It explains how to compare explosives based on their properties like strength, detonation velocity, density etc. It describes drilling systems and the theory of rock breakage through radial cracking and flexural rupture. Finally, it discusses blast design factors and different controlled blasting techniques like line drilling, cushion blasting, smooth-wall blasting and pre-splitting used to control overbreak.
The document provides an outline for a course on quantum mechanics. It discusses key topics like the time-dependent Schrodinger equation, eigenvalues and eigenfunctions, boundary conditions for wave functions, and applications like the particle in a box model. Specific solutions to the Schrodinger equation are explored for stationary states with definite energy, including the wave function for a free particle and the quantization of energy for a particle confined to a one-dimensional box.
6th Training Course on Radiation Protection for Radiation Workers and RCOs of BAEC, Medical Facilities & Industries
Training Institute, AERE, Savar, BAEC
24 - 29 October 2021
IRJET- Automatic Footbridge Platform System on Railway PlatformIRJET Journal
This document describes a proposed automatic footbridge platform system for railway stations. The system aims to make crossing between platforms safer and more convenient. It would involve attaching sliding platforms between the two stationary platforms that can be adjusted based on train presence and movement. Sensors and motors would allow the sliding platforms to open when it is safe to cross, and close when a train is approaching or present. This proposed system could help reduce accidents, save time for passengers crossing between platforms, including those with limited mobility, and reduce electricity usage compared to existing solutions like escalators. It provides a potential safer and more efficient way to facilitate passenger movement at railway stations.
Nuclear Isomerism
A nuclear isomer is a metastable state of an atomic nucleus caused by the excitation of one or more of its nucleons (protons or neutrons). "
"Metastable" refers to the property of these nuclei whose excited states have half-lives longer than 100 to 1000 times the half-lives of the excited nuclear states that decay with a "prompt" half life (ordinarily on the order of 10−12 seconds). As a result, the term "metastable" is usually restricted to isomers with half-lives of 10−9 seconds or longer.
Augar Effect
The transition of a nucleus from an excited to the ground state may occur by the EJECTION OF ORBITAL ELECTRONS
It is an alternative GAMMA emission
IF the energy TRANSFERRED to the electrons in this process exceeds the electron binding energy EB ,The electron is ejected with a kinetic ENERGY
Ee =E - EBThe transition of a nucleus from an excited to the ground state may occur by the EJECTION OF ORBITAL ELECTRONS
It is an alternative GAMMA emission
IF the energy TRANSFERRED to the electrons in this process exceeds the electron binding energy EB ,The electron is ejected with a kinetic ENERGY
Thankyou....
Presentation of PhD Thesis: "A perspective on metasurfaces, circuits, holograms and invisibility". Carlo Andrea Gonano, Politecnico di Milano, Italy, 26 January 2016.
This document discusses methods for measuring the velocity of detonation (VOD) of explosives. It describes several point-to-point and continuous methods, including the electric probe method, D'autriche method, resistance wire system, SLIFER system, and TDR system. The electric probe method uses probes placed in the explosive at set distances to measure the time for detonation to travel between them. The D'autriche method calculates VOD based on the proportional VOD of a detonating fuse. Resistance wire and the SLIFER and TDR systems monitor changes in a sensor like a wire or cable as detonation consumes it to determine VOD.
This document discusses key aspects of safely transporting radioactive material as outlined in international regulations. It covers material classification, package selection based on material type and content limits, and controls during transport including limits on radiation levels, transport indexes, and categorizing packages. The overall safety approach involves containing radioactive contents, controlling external radiation, preventing criticality, and preventing heat damage through a graded package design based on material hazard levels.
This document is a project report submitted by Priyanka Verma and Smriti Singh for their Bachelor of Science degree in physics. It discusses elementary particles, including their characteristics, classification, conservation laws, and examples like electrons, positrons, protons, neutrons, pions, and kaons. The report includes certificates of completion from their college principal and physics professors.
Plasma is one of the advanced technology in semi conducting materials. Scientists states that 99% of the universe is covered with plasma. Plasma Antenna is a special type of antenna in which metal conducting elements of conventional antenna are replaced by plasma. Its 4th state of matter similar to gas. It employs ionized gas enclosed in a tube as conducting element of an antenna. When the gas is electrically charged or ionized to plasma, it becomes conductive & allowing radio frequency signals to be transmitted or received. When gas is not ionized, the antenna elements ceases to exit. When voltage is applied to an antenna, electric field is produced which causes current to flow in antenna. Due to current flow, magnetic field is produced. It is more advantageous than other antenna due to ionized gas. It has higher effiency & enhanced bandwidth. The fact that the emitting element is formed over the interval needed for the emission of an electromagnetic pulse is an important advantage of plasma antennas . In the passive state (in the absence of plasma in the discharge tube),such a device does not exhibit electric conductivity. A plasma stream flowing from a jet into the ambient space , the plasma trace of a body moving at an ultrasonic velocity in the atmosphere , and alternative plasma objects have been studied as possible antenna elements.
Metal antennas currently in implementation use metallic conductor as guiding medium for electromagnetic radiations. Plasma antennas uses ionized medium. The plasma antenna is a radiofrequency antenna formed by a plasma columns, filaments or sheets, which are excited by a surface wave. The relevance of this device is how rapidly it can be turned on and off only applying an electrical pulse. Unlike traditional metal antenna, plasma antenna is based on partially or fully ionized gas used as a conducting material
Plasma antennas find its applications in variety of fields due its unique properties, characteristics and advantages over traditional metallic antennas.
i) Faster internet
ii) Public safety networks
iii) Radio and television broadcasting
iv) Space communication
This document provides an overview of plasma physics and its applications. It introduces plasma as the fourth state of matter and discusses its fundamental properties and types. The document outlines various methods for plasma formation, including passive thermal ionization and active generation using external energy sources. Atmospheric and vacuum plasma generation techniques are examined, along with their applications in science, technology, and industry. The document concludes that plasma physics remains an interesting field with opportunities for new discoveries.
DOWNLOAD THE POWERPOINT FILE FROM HERE:
https://www.dropbox.com/s/d8zbqyvc81pgg5w/compton%20effect.pptx?dl=0
Describing Compton Effect from Quantum Mechanics. Presented in East West University.
The document discusses the photoelectric effect and its applications. It begins by explaining Einstein's theory that light consists of quantized packets of energy called photons and how this explains the photoelectric effect. It then discusses how the kinetic energy of emitted electrons increases with higher frequency light. The document also provides a simple diagram of a photoelectric experiment and describes some common applications of the effect, including night vision devices, cameras, and smoke detectors. It ends by showing an image and further explaining how photoelectric smoke detectors work by detecting light scattered by smoke particles.
The document discusses the density of states in two-dimensional systems. It explains that the density of states function describes the number of available energy states in a system and is essential for determining carrier concentrations and distributions. In semiconductors, carrier motion is limited to two, one, or zero spatial dimensions, requiring the density of states to be known in quantum wells (2D), quantum wires (1D), and quantum dots (0D). The document then focuses on the density of states in 2D systems, noting that it is independent of energy and depends on the number of quantized levels in the confined dimension.
There are three main types of laser gain media: gases, liquids, and solids. Gases like CO2 have narrow wavelength gain, while liquids like dyes have broad gain. Solid state lasers like Nd:YAG can have either narrow or broad gain depending on the material. All gain media require pumping to receive energy, which can be optical pumping using lamps or flashlights, or electrical pumping using gas discharges. Q-switching is a technique to produce high power pulses using a Pockels cell to prevent lasing until a population inversion is fully inverted.
Dye lasers use an organic dye dissolved in a liquid as the active lasing medium and can produce a wide range of wavelengths. They work on the principle of population inversion using a pumping source like a flash lamp or other laser to excite the dye molecules. The major components are the active dye medium, pumping source, and resonator mirrors, with one mirror sometimes replaced by a diffraction grating to allow tuning of the output wavelength. Dye lasers offer tunability but have limitations in lifetime and output power.
Explosives, Theory Of Breakage And Blasting Operationspartha sharma
This document discusses explosives and blasting operations. It defines different types of explosives and their ingredients and functions. It explains how to compare explosives based on their properties like strength, detonation velocity, density etc. It describes drilling systems and the theory of rock breakage through radial cracking and flexural rupture. Finally, it discusses blast design factors and different controlled blasting techniques like line drilling, cushion blasting, smooth-wall blasting and pre-splitting used to control overbreak.
The document provides an outline for a course on quantum mechanics. It discusses key topics like the time-dependent Schrodinger equation, eigenvalues and eigenfunctions, boundary conditions for wave functions, and applications like the particle in a box model. Specific solutions to the Schrodinger equation are explored for stationary states with definite energy, including the wave function for a free particle and the quantization of energy for a particle confined to a one-dimensional box.
6th Training Course on Radiation Protection for Radiation Workers and RCOs of BAEC, Medical Facilities & Industries
Training Institute, AERE, Savar, BAEC
24 - 29 October 2021
IRJET- Automatic Footbridge Platform System on Railway PlatformIRJET Journal
This document describes a proposed automatic footbridge platform system for railway stations. The system aims to make crossing between platforms safer and more convenient. It would involve attaching sliding platforms between the two stationary platforms that can be adjusted based on train presence and movement. Sensors and motors would allow the sliding platforms to open when it is safe to cross, and close when a train is approaching or present. This proposed system could help reduce accidents, save time for passengers crossing between platforms, including those with limited mobility, and reduce electricity usage compared to existing solutions like escalators. It provides a potential safer and more efficient way to facilitate passenger movement at railway stations.
Nuclear Isomerism
A nuclear isomer is a metastable state of an atomic nucleus caused by the excitation of one or more of its nucleons (protons or neutrons). "
"Metastable" refers to the property of these nuclei whose excited states have half-lives longer than 100 to 1000 times the half-lives of the excited nuclear states that decay with a "prompt" half life (ordinarily on the order of 10−12 seconds). As a result, the term "metastable" is usually restricted to isomers with half-lives of 10−9 seconds or longer.
Augar Effect
The transition of a nucleus from an excited to the ground state may occur by the EJECTION OF ORBITAL ELECTRONS
It is an alternative GAMMA emission
IF the energy TRANSFERRED to the electrons in this process exceeds the electron binding energy EB ,The electron is ejected with a kinetic ENERGY
Ee =E - EBThe transition of a nucleus from an excited to the ground state may occur by the EJECTION OF ORBITAL ELECTRONS
It is an alternative GAMMA emission
IF the energy TRANSFERRED to the electrons in this process exceeds the electron binding energy EB ,The electron is ejected with a kinetic ENERGY
Thankyou....
2. Ana Hatlar
1. Bazı Temel Simetriler
2. Süpersimetri (SUSY)
2.1 Önemli Motivasyonlar
2.2 SParçacıklar
2.3 Temel Prensipler
2.4 Wess-Zumino Modeli
3. Süpersimetrik Kozmoloji
4. Karanlık Madde Adayı Süpersimetrik
Parçacıklar:
• Nötralino
• Gravitino
• Aksino
3. 1. Bazı Temel Simetriler
Simetri Nedir?
Belirsiz bir mükemmellik veya güzelliği yansıtan, estetik olarak hoşa
giden bir orantılılık ve denge duygusudur.
Matematikte Simetri Nedir?
Bir objenin verilen bir matematiksel işleme göre simetrik
(değişmeden) kalması simetriyi gösterir.
g : G × X → X
4. 1. Bazı Temel Simetriler
Örnek 1: (D3)
r: O merkezi etrafında dönmeler
s: Kenarortay etrafında dönmeler
Etkisiz eleman: r0
= r3
= s0
= s2
= e
Her elemanın tersi vardır: r2
.r = e
Birleşme özelliği vardır:
r(r2
s) = (r.r2
)s = r3
s = es = s
Kapalılık özelliği vardır:
Grup işlemi yoluyla grup elemanları
dışında elemanlar elde edilemez.
GRUP AKSİYOMLARI sağlanır.
e r r2
s rs r2
s
e e r r2
s rs r2
s
r r r2
e rs r2
s s
r2
r2
e r r2
s s rs
s s r2
s rs e r2
r
rs rs s r2
s r e r2
r2
s r2
s rs s r2
r e
5. 1. Bazı Temel Simetriler
Örnek 2: (S3) permütasyon grubunun elemanları,
veya e, (12), (13), (23), (123), (132)
S3 ve D3 arasındaki izomorfizmi gösterelim:
e → e (23) → s
(123) → r (12) → rs
(132) → r2
(13) → r2
s
e (123) (132) (23) (12) (13)
e e (123) (132) (23) (12) (13)
(123) (123) (132) e (12) (13) (23)
(132) (132) e (123) (13) (23) (12)
(23) (23) (13) (12) e (132) (123)
(12) (12) (23) (13) (123) e (132)
(13) (13) (12) (23) (132) (123) e
=
213
321
,
132
321
,
231
321
,
123
321
,
312
321
,
321
321
e
6. 1. Bazı Temel Simetriler
Örnek 3: (Rubik Küp)
Tüm hamleler sınıflandırılarak
4 çeşit temel hamleye indirgenebilir :
• Köşe Kübitlerin poziyonunu (S8)
• Kenar Kübitlerin pozisyonunu (S12)
• Köşe Kübitlerin yönelimini (Z3
8
)
• Kenar kübitlerin yönelimini (Z2
12
)
değiştiren hamleler ve bileşik hamleler.
Rubik Kübün Grup Yapısı:
“Griess” notasyonunda
Küp grubunun derecesi~ 4x1019
Optimal çözüm hamle sayısı < 20
Soru: N < 20 olacak şekilde yapılacak optimal çözüm nedir??
Ara Sonuç: Simetriler hakkında hala bilmediklerimiz
var.
7. 1. Bazı Temel Simetriler
Simetriler hakkında bildiklerimiz:
• Doğada simetriler kırılabilir.
• “Fizik yasalarının” simetrik yapısı da doğaya uygun
olarak kırılabilmelidir. (Örn: Süreksiz simetriler)
• Matematikte simetriler, ilgili oldukları dönüşümlerle
önemli grup yapılarını indükler. (1960 – 1980, >10.000
grup teori makalesi var)
• Standart Model (SM) parçacıkların ayar grup yapısının
SU(3)xSU(2)xU(1) olduğunu göstermiştir. Bu sonuca
“Gravitasyon alanı” dahil değildir.
• “Noether Teoremi”
8. 1. Bazı Temel Simetriler
• C: Charge, P: Parity, T: Time
• Scale (Ölçek) simetrisi → Konformal Alan Teorisi
• Ayar Simetrisi → Kuantum Alan Teorisi
SİMETRİLERSİMETRİLER
Kesikli Simetriler Sürekli Simetriler
CPT simetrisi Uzay-zaman simetrileri Dahili Simetriler
İzospin, baryon sim…vs.
Yerel Simetriler:
SU(3)c , U(1)em , SU(2)L
Global Simetriler
Φ -> e(..)
Φ
9. 2. Süpersimetri (SUSY)
“Standart Model Parçacık
Havuzu”
4 Etkileşim Alanın Bozonları
(Kuvvet taşıyıcılar):
Güçlü → gluon
Zayıf → W±
,Z
E.Magnetik → Foton
Gravitasyon → Graviton
10. 2. Süpersimetri (SUSY)
“Süpersimetri, fermiyon ve bozon durumları arasında, bir Q
operatörüyle ile tanımlanan dönüşümlere bağlı uzay zaman
simetrisidir. Bu dönüşümlere süpersimetrik dönüşümler denir.”
(Martin F. Sohnius) nB = nF
Clifford Cebri:
V:Vektor uzayı, F: C alan
Q(λ) = λ2
Örn: Dirac Matrisleri
Coleman-Mandula teoreminin Haag-Lopuszanski-Sohnius
tarafından ortaya atılan açılımına göre SUSY bir Lie super cebri
olduğu için mümkündür.
BozonFermiyonQ =FermiyonBozonQ =
12. 2. Süpersimetri (SUSY)
Süpermultiplet: Bir süpersimetrik teorideki tek-parçacık durumunun
süpersimetrik cebre göre indirgenemez tek temsilidir. Her
supermultiplet içinde fermiyon ve bozon durumları vardır.
Süpermultiplet içindeki parçacıklar birbirinin süper eşidir.
Q ve Q+
süpersimetri jeneratörleridir. Süpersimetrik modeller bu
jenaröterlerin sayısına göre N = 1, 2, 3..vs. isimlendirilirler.
P, uzay-zaman
dönüşümlerinin
4lü momentum
jeneratörü
Noether Teoremine göre Süperakım korunur.
0],[],[
0},{},{
},{
==
==
=
+
++
+
QPQP
QQQQ
PQQ
µµ
µ
13. 2.1 Önemli Motivasyonlar
SM’de Serbest Parametreler
• 3 ayar çiftlenim sabiti
• Yukawa sabiti λ ve kütle m (Higgs sektörüne ait)
• 6 kuark (u,d,c,s,t,b) ve 3 lepton (e,μ,τ) kütlesi
• 3 karışım açısı
• 1 CP-ihlali fazı (Kuark sisteminde)
• 1 QCD çiftlenim parametresi θ
+--------------------------------------
• Toplam 19 parametre ! Daha az sayıda serbest
Parametre olabilir mi?
• Ayar Hiyerarşi Problemi
• SM Karakteristik enerji ölçeği: MW ~100 GeV
• Gravitasyon Karakteristik enerji ölç.: MP ~ 1019
GeV
• Skaler Bozon kütlelerinin kuadratik ıraksaması
14. Nötrino Salınımları (Deneysel Kanıt)
Nötrinoların çeşni(kütle) ve etkileşme arasındaki ilişki
α = e (elektron) , μ (muon) , τ (tau) ->
Kütle özdurumları
i = 1, 2, 3 -> Etkileşme özdurumları
U = Maki-Nakagawa-Sakata karışım
matrisi (MNS)
Deneyler:
MiNiBooNe , K2k , Kamiokande
Sonuç:
Nötrinolar kütleli !
2.1 Önemli Motivasyonlar
α
α
α
αα
νν
νν
∑
∑
=
=
ii
i
i
i
U
U *
dlvW +→+
α
15. Nötrino kütleleri (Seesaw Mechanism):
Lagranjiende Dirac Kütle terimleri Majorana Kütle terimleri
L,R nötrino helisite durumları, C yük konjugasyonu ve
Bütün terimleri matris notasyonunda tek bir Lagranjiende
toplarsak;
Kütle matrisinin öz değerleri yaklaşık
m ~ 10-2
GeV alınırsa M ~ 1014
GeV !
2.1 Önemli Motivasyonlar
17. 2.3 Temel Prensipler
dönüşümlerini Є1 ve Є2 şeklinde çift spinörlü
yazdığımızda cebrin kapanması için aşağıdaki şartın sağlanması gerekir:
Buna kabuk durumunda (on-shell) cebrin kapanması denir. Ancak
süpersimetri cebri kabuk dışı (off-shell) için de kapanmalı. Bunu
sağlamak için Lagranjiene yardımcı yeni bir alan eklememiz gerekir.
W; süpersimetrik potansiyel olarak adlandırılır. Süpersimetrik modeller W
seçimine bağlı olarak oluşturulur.
18. 2.4 Wess-Zumino Modeli
Kütlesiz ve Lagranjieni etkileşim içermeyen en basit süpersimetrik modeldir.
Doğal olma problemine aşağıdaki gibi çözüm getirir.
1. İki serbestlik derecesine sahip bir kompleks skaler alan için
2. İki serbestlik derecesine sahip Majorana spinörüyle tanımlı bir fermiyon alanı
Lagranjiendeki kinetik terim;
Lagranjiendeki etkileşim terimi; Süperpotansiyel;
Son ifadeden aşağıdaki diagramlar için köşe faktörlerini yazıp genliğe
gelecek katkıları hesaplayalım…
2/)( iBA +=φ
ψψψ == TC
C
ψγψψγψφφ ν
ν
µ
µ
µ
µ
ν
ν
µ
µ
∂+∂∂+∂∂=∂+∂∂=
22
1
2
1
2
* i
BBAA
i
Lk
+−−= RLLRi
d
Wd
d
Wd
d
dW
L ψψ
φ
ψψ
φφ 2
2
2
22
2
1 32
3
1
2
1
)( λφφφ += mW
ψγψ
λ
ψψ
λλ
)(
22
1
)(
4
)(
2
)(
2
1 5222
2
22222
iBAmBABAA
m
BAmLi −−−+−+−+−=
20. 3. Süpersimetrik Kozmoloji
Big Bang: Evrenin son derece yoğun ve sıcak bir “tekillik”
sonrası genişleyerek oluştuğunu savunur.
Olbers Paradoksu: (1823) Sonsuz sayıda yıldız olmasına rağmen
evren neden karanlıktır?
1. Evren gençtir ve yalnızca 10 milyar yıldır ışık saçmaktadır.
2. Evren termodinamik dengeden kaçınacak biçimde
genişlemektedir.
→ D: Uzaklık, v: Hız, H: Hubble sbt. ~ 70.1 ± 1.3
km/s/Mpc
DHv 0=
=−=−= ρ
πρπ 3
2
3
4
,
3
4
.. RM
GmR
R
mMG
EP
22
2
1
.. RmHEK =
G
H
EPEK
π
ρ
8
3
..
2
=⇒=
330
/105.4 cmgc
−
×=ρKritik Yoğunluk: Ω≡
cρ
ρ
21. 3. Süpersimetrik Kozmoloji
Düzlük Problemi: Sürekli
genişleyen evren yüzeyi giderek
düzleşerek düz evren modeli ile
ayırt edilemez olmuştur.
Kritik yoğunluktaki bir evren
modelinde “WIMP” olmak
zorundadır !
Anlamlı Sayılar: Kozmolojik parametrelerin dahil olduğu sınırlardır.
22.0 0 ≤Ω≤
22. MSSM: Süpersimetri kırılmasının açıklandığı ve ayrıntılı süperpotansiyellerin
yazıldığı supersimetrik modeldir. Başlangıç için süper potansiyel;
alınabilir ve kiral süpermultipletlere karşılık gelen alanlar
olarak düşünülebilir.
Ancak toplam potansiyel içinde Baryon ve Lepton korunum yasalarına
uymayan aşağıdaki terimler de vardır,
Baryon – Lepton korunumunu sağlamak için aşağıdaki gibi bir kuantum sayısı
tanımlanır; (R-parite)
3. Süpersimetrik Kozmoloji
23. 3. Süpersimetrik Kozmoloji
R-paritesinin korunumunun önemli sonuçları vardır:
1. PR=-1 paritesine sahip olan en hafif s-parçacık (LSP) kesinlikle
stabil olmalıdır. Eğer elektriksel olarak nötral ise sadece sıradan
madde ile etkileşime girer. LSP, bu özelliği ile non-baryonik kara
cisim için iyi bir adaydır.
2. LSP dışındaki s-parçacıklar hemen (anında) tek sayıda LSP
içeren durumlara bozunmalıdır. (genellikle tek bozunma)
3. Çarpıştırıcı deneylerinde, s-parçacıklar çiftler halinde
üretilmelidir.
Madde Paritesi : R-paritesinin spin etkisini göz ardı eden şekli
olarak bilinir.
Her iki korunum yasası da MSSM içinde açıklanmaktadır. Fakat
MSSM’in bazı açılımlarında R-parite korunumu ihlal edilir,
alternatif korunumlar ortaya konur ya da bu simetrinin kırıldığı
söylenir.
24. 4.Karanlık Madde
Karanlık Madde: Büyük Patlama teorisine göre evrenin
oluşumundan bu yana hiçbir maddeyle doğrudan etkileşime
girmeyen ve gözlenemeyen kayıp maddedir.
Evrendeki kayıp maddenin varlığı ayrıntılı gravitasyon
hesaplamalarıyla ilk defa 1933 de Fritz Zwicky tarafından
farkedilmiştir.
Karanlık maddenin varlığı Büyük Patlamanın varlığı ile birlikte
1965 yılında Kozmik Mikrodalga Fon ışınımı (CMB) yoluyla
gösterilmiştir. Bu ışınım 2.725°K ısısında, 160.2 GHz frekansla
1.9mm dalga boyuna sahiptir.
25. 4.Karanlık Madde
Karanlık maddenin yapısında olabileceği düşünülen
parçacıklar şunlar;
Baryonik Karanlık madde: Rydberg maddesi.
Non-Baryonik Karanlık madde:
Sıcak Karanlık madde: Ultra göreli hızlardaki non-baryonik
parçacıklar
Ilık Karanlık Madde: Göreli hızlarda hareket eden non-
baryonik parçacıklar
Soğuk Karanlık Madde: Düşük hızlarda hareket eden non-
baryonik parçacıklar
Non-Baryonik Soğuk karanlık madde kapsamında
aşağıdaki süpersimetrik parçacıkların iyi birer aday
oldukları bilinmektedir:
Nötralino
Gravitino
Axino
26. 4.1. Nötralino
• MSSM’de Süpersimetrinin kırılmasıyla birlikte (Standart Modelde
olduğu gibi) yeni bozonlar kütle kazanır.
• Standart Modelde, W+
W-
ve Z0
bozonlarının süper eşleri SUSYde
yüklü chargino ve yüksüz nötralino parçacıklarıdır.
• Yüksüz olması, az etkileşmesi ve en hafif s-parçacık olarak
öngörülmesi nedeniyle nötralino kara madde adayı
parçacıktır.
• Kütlesinin ~100 GeV mertebelerinde olacağı öngörülmektedir.
• Şimdiye kadar TEVATRON ve LEP
deneylerinde gözlenememiştir,
nedeni dedekte edilmekten kaçması
ve bir enine enerji bileşenine ET
sahip olmasıdır.
• LHC deneyinin ilk bulgularından
biri olacağı düşünülmektedir.
0~
lχ +
lχ~ −
lχ~
0~
lχ
29. 4.2. Gravitino
•Gravitino, spini 2 olan kütle çekim ara parçacığının gravitonun
süpersimetrik eşidir.
•Gravitino, Süpersimetride global simetriden lokal simetrilere
geçildiğinde ortaya çıkacak Süpergravitasyon (SUGRA) alanının
öncü parçacığıdır.
•SM ayar grubuna göre gravitino parçacığı singlettir ve
etkileşmeleri süpergravite Lagranjieni ile elde edilebilir.
•Eğer gravitino varsa bu bir spin 3/2 vektör-fermiyondur ve
böylece Rarita-Schwinger denklemine uyar.
•Stabil yada Unstabil olacağı iki durum öngörülmektedir.
Gravitino; ancak stabil parçacıksa karanlık madde adayı olabilir.
•En önemli etkileşmesi; ττ G
~~ →
LR τϕτϕτ ττ
~)sin(~)cos(~ +=
]~)~()~[(
2
1 *
2/3
µν
µνµ
νµ
ν ψγγτττγγψτ LRRR
P
PDPD
M
L +−=
RR ieAD ττ ννν
~)(~ +∂= GeVxGM NP
182/1
10436.2)8( == −
π
2/33 mMM PSusY =
30. 4.2. Axino
QCD’de CP-simetrisinin bozulması “güçlü CP-bozulması” olarak
adlandırılır.
Lagranjienin son terimindeki θ sabiti CP bozulmasına yol
açmaktadır.
Peccei-Quinn Mekanizması olarak bilinen teoriye göre θ, dinamik
bir alan olarak tanımlanır ve karşılık gelen parçacığa “axion” adı
verilir. Bu alanın getirdiği potansiyel ifadesi son terimin
sadeleşmesini sağlar.
Axino; “axion” parçacığının süpersimetrik eşidir. (spin=1/2)
31. Sonuçlar
• Gelecek senelerde SUSY ve diğer simetriler
deneysel ve teorik anlamda araştırılmaya devam
edecektir.
• Karanlık Maddenin ne olduğunun belirlenmesi
Kozmoloji ve YEF alanında devrim niteliği
taşıyacaktır.
• SUSY deneysel olarak doğrulanmasa bile Fiziğe
katkısı tartışılmaz derecede büyüktür.
33. • Supersymmetry (Oxford Graduate Texts) Pierre Binetruy – Oxford 2006
• A Supersymmetry Primer (hep-ph/970376) Stephen P. Martin – 2006
• Sparticles (World Scientific Press) M. Drees, R.Godbole, P. Roy – 2006
• Introducing Supersymmetry () Martin F. Sohnius –
• Supersymmetry (North-Holland Publishing Co.) P.Fayet, S.Ferrara – 1976
• Prospects to study a long-lived charged Next Lightest Supersymmetric
Particle at LHC (SISSA ) K.Hamaguchi, M.Nojiri, A.Roeck – 2007
• Supersymmetric Dark Matter Candidates (hep-ph/1240) D.Steffen – 2007
• Supergravity at Colliders (Physics Letters) W.Buchmüller, K.Hamaguchi,
M.Ratz, T.Yanagida – 2004
• "To name something is not generally to understand it."
• Innumeracy: Mathematical Illiteracy and its Consequences(1988)-John
Allen Paulos
Referanslar
