• • • Part of the book series (NAII, volume 72) Abstract The name of the technique takes its origin in 1964 paper of L. Among the earlier closely related approaches, one should mention J. Schwinger [ ] and R. Feynman and F. Classical counterparts of the Keldysh technique are extremely useful and interesting on their own.

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I shall mention Wyld diagrammatic technique [ ], which is the basis of the modern theory of turbulence; Martin-Siggia-Rose-DeDominics method [ ] for stochastic systems; and Doi-Peliti technique [, ] for reaction-diffusion systems and cellular automata. Despite the unique power and wide popularity of the technique its pedagogical presentations are rare. One may find some in books [, ] or in a review [ ]. This lecture is not an alternative for the existing literature. Using the simplest possible example, I try to explain the general structure of the theory, its relation to other approaches, its potential for novel applications and open problems. Technicalities of the numerous practical applications may be found in the literature and left outside the scope of the lecture. I tried hard, however, to mention possible traps and silent points which are rarely exposed explicitly.

Cite this chapter as: Kamenev A. (2002) Keldysh and DOI-Peliti Techniques for Out-of-Equilibrium Systems. In: Lerner I.V., Althsuler B.L., Fal’ko V.I., Giamarchi T.

(eds) Strongly Correlated Fermions and Bosons in Low-Dimensional Disordered Systems. NATO Science Series (Series II: Mathematics, Physics and Chemistry), vol 72.

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Springer, Dordrecht • DOI • Publisher Name Springer, Dordrecht • Print ISBN 978-1-4020-0749-1 • Online ISBN 978-94-010-0530-2 • eBook Packages • •.