A basic introduction to Keldysh techniques is given.

1. Introduction to Keldysh technique
Krzysztof Pomorski
University of Warsaw, Faculty of Physics
kdvpomorski@gmail.com
June 10, 2014
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2. Overview
1 Equilibrium Green function
2 Keldysh contour
3 Application of Keldysh technique
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3. Equilibrium Green functions
iG(x, t; x , t ) =< φ0|T(ψ(x, t)ψ†
(x , t ))|φ0 > (1)
iG(x, t; x , t ) =
< φ0|S(+∞, −∞)ψ(x, t)ψ†(x , t )|φ0 >
< φ0|S(+∞, −∞)|φ0 >
(2)
S(+∞, −∞) = T exp(−i
+∞
−∞
dt1V (t1)) (3)
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4. Keldysh contour
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7. Green function
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9. Green functions on Keldysh contour
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10. Larkin representation
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11. Some identities among Green functions
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14. Green functions equations of motion on Keldysh contour
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16. Keldysh Green functions
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17. To be remembered...
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28. References
An Introduction to Nonequilibrium Green Functions,
Robert van Leeuwen and Nils Erik Dahlen, 2005
Keldysh technique and nonlinear sigma-model:basic principles and applications,
Alex Kamenev and Alex Levchenko, 2009
An introduction to nonequlibrium many-body theory,
Joseph Maciejko, 2007
Quasiclassical equations of the theory of superconductivity for contiguous metals
and the properties of constricted microcontacts,
A.V.Zaitsev, 1984, Zh. Eksp. Teor. Fiz. 86
Quantum theory of nonequilibrium processes,
P.Danielewicz, 1983
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29. The End
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