Question

I'd like some suggestions for good reading materials on the Keldysh formalism in a condensed matter context. I'm familiar with the imaginary time, coherent state, and path integral formalisms, but lately I've been seeing Keldysh more and more in papers. My understanding is that it is superior to the imaginary time formalism at least in that one can evaluate non-equilibrium expectations.

Answer 1

I am somewhat biased towards condensed matter physics, even though the subject extends also to fields such as cosmology and QCD.

In the context of condensed matter physics I recommend the following books (even though various techniques also apply outside this regime):

Rammer's Quantum Field Theory of Non-Equilibrium States. This was my first read on it, and I was quite content with it. If you are familiar with the idea of using periodic imaginary time to simulate a temperature then this book will explain the small additional step you need to take to grasp the basics of the Keldysh formalism. Unfortunately it's just formalism for the first 7 (!) chapters and sometimes the pace is a bit slow.

Kadanoff and Baym's Quantum Statistical Mechanics: Green's Function Methods in Equilibrium and Nonequilibrium Problems. A classic.

Kubo, Toda and Hashitsume's Statistical Physics II: Nonequilibrium Statistical Mechanics. Has some elements of classical statistical physics as well. The authors are very insightful.

There's also chapter 18 in Kleinert which I find a nice read. This book is huge though and treats a lot of other topics. Still, if you go through Rammer then this chapter by Kleinert nicely summarizes everything without dropping too many details. The newest edition of Altland and Simons has two chapters on classical and quantum systems out of equilibrium, but I was fairly disappointed with their treatment considering the rest of the book is fantastic.

As for quantum transport, where this formalism is frequently employed, I can recommend Di Ventra as an undergrad-level introductory book and this book by Datta for some other interesting topics. Weiss is excellent for dissipative (open) systems, although this field opens up a whole new can of worms so you might want to avoid at first.

Other sources not in book form:

Rammer and Smith's review article "Quantum field-theoretical methods in transport theory of metals" (Rev. Mod. Phys. 58 no. 2, 323