Quantum cosmology and boundary conditions from algebraic lines...; building upon a vintage conjecture from B DeWitt (1967...)

1. Paulo Moniz
CMA-UBI
&
CMS, DAMTP(sabbatical)
Upon a vintage conjecture

2. ive ct
(recent) Results in quantum cosmology
intertwining
boundary conditions,
the algebra of constraints
(hidden) symmetries
very simple toy model
Outlook
Currently in progress
(slow...)
(tentative) Outline

3. Boundary conditions
(physical) Laws that determine how, from an initial state, to
proceed to subsequent states.
In classical physics, if the initial state of a system is
specified, then the subsequent motion will be completely
predictable*.
In quantum physics, specifying the initial state of a system
allows one to calculate the probability that it will be found
in any other state .
Quantum cosmology is
based on the idea that
quantum physics should
apply to everything in
nature, including the
whole universe

4. Boundary conditions
No-boundary
Tunneling
‘DeWitt’
...

5. Cosmology and General Relativity

6. Classical Model

7. Classical Model

8. Classical Model

9. Classical Model

10. Classical Model

11. QUANTIZATION AND DIRAC OBSERVABLES
Standard quantization (of this simple system):
coordinate representation
Wheeler–DeWitt equation
Assume wave functions defined on the
x € [x_o, ∞) domain
... self-adjoint Hamiltonian.

12. QUANTIZATION AND DIRAC OBSERVABLES

13. Reduced phase space and observables
GR is invariant under the group of diffeomorphisms on
the spacetime manifold M.
The Hamiltonian can be expressed as a sum of
constraints;
any observable must commute with these constraints.
An observable is a function on the constraint surface;
it is invariant under the gauge transformations;
generated by first-class constraints.

14. Reduced phase space and observables

15. Reduced phase space and observables
The Hamiltonian constraint implies
Furthermore, we have
where j={1/4,3/4} denote the Bargmann indices for
the harmonic oscillator.

16. Reduced phase space and observables
which consequently implies that the Bargmann index
is a gauge-invariant observable:

17. Hidden symmetry and boundary conditions
Subsystems ← from observations outside of the subsystem;
(... rest of the universe)
Quantum cosmology: specifications cannot be passed off to
the ‘rest’ of the universe’’.
DeWitt’s vintage conjecture: “The cosmological boundary
condition must be one of the fundamental laws of physics”

18. Hidden symmetry and boundary conditions
su(1,1) Lie algebra

19. Hidden symmetry and boundary conditions
where j={1/4,3/4}

20. Hidden symmetry and boundary conditions

21. Hidden symmetry and boundary conditions
From one of the papers:

22. Intermezzo
Selection of boundary proposals
Related to the Dirac observables
Reduced phase space quantization
Hidden symmetry su(1,1)
Dirac observable related to the boundary proposals

23. References
1. Dirac observables and boundary proposals in quantum cosmology.
Phys. Rev. D 89, (2014) 083504; S. Jalalzadeh and P. V. Moniz
2. On the relation between boundary proposals and hidden symmetries of the extended pre-big
bang quantum cosmology
Eur. Phys. J. C 75 (2015) 38; S. Jalalzadeh, T. Rostami, P. V. Moniz
3. Quantum cosmological intertwining: Factor ordering and boundary
conditions from hidden symmetries
Phys. Rev. D. 92 (2015) 023526; T. Rostami, S. Jalalzadeh, P.V. Moniz
4. Quantum Cosmology: From hidden symmetries towards a new (supersymmetric) perspective
(Invited review article)
In. J. Mod. Phys. D 25, 1630009 (2016); S. Jalalzadeh, T. Rostami and P.V. Moniz,
5. Quantum Cosmology - The Supersymmetric Perspective - Vol. 1 and Vol. 2
https://www.springer.com/gp/book/9783642115745
https://www.springer.com/gp/book/9783642115691
P.V. Moniz
6. Challenges in quantum cosmology.
(2020) S. Jalalzadeh and P. V. Moniz

24. Picard – Lefschetz
Thimbles…
NBWF…
Witten (index)
SUSY-QM & homology
Quantum entanglement
Quantum chaos
2+1 & spatial varying dimentions (fractal qm)
Quantum gravity corrections
Quantum groups
‘Swampland’ & “DeSitter” (or not...)
Outlook (in progress)
Email: pmoniz@ubi.pt; prlvm10@cam.ac.uk
https://www.linkedin.com/in/pvmoniz/
(https://www.dfis.ubi.pt/~pmoniz/)