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I am looking for an introductory textbook on QFT in curved space-time via the path integral method. I want to understand the following:

  • How to build a generic perturbative QFT in curved space-time
  • Are there some specific difficulties with normalization
  • How to derive observables / particle states in curved space-time
  • The Unruh effect
  • The Hawking radiation

I would appreciate if the author would use path integrals instead of the canonical formalism when possible. The reason for this is purely aesthetic.

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  • $\begingroup$ There's a comprehensive book on path integrals by Kleinert, which discusses quantization on curved manifolds (chapter 10 of 'Path Integrals in Quantum Mechanics [etc.]'). Wald's GR textbook also has a chapter on QFT in curved spacetime, and Carroll's textbook has a clear explanation of the Unruh effect. $\endgroup$
    – TLDR
    Commented Jun 29, 2015 at 16:32
  • $\begingroup$ Related: physics.stackexchange.com/q/110763/2451 and links therein. $\endgroup$
    – Qmechanic ♦
    Commented Jun 29, 2015 at 17:04

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I would suggest one of the (standard) books (though somehow old) on QFT in curved spacetime,

  • Quantum Fields in Curved Space (Birrel & Davies) Relates to path integral formalism, and covers a lot of topics in QFT on curved spacetime
  • Quantum Field Theory in Curved Spacetime (Parker & Toms) Uses DeWitt notation, a lot based on effective action derived from some path integral, very good book treating also black holes
  • [Quantum field theory in curved spacetime and black hole thermodynamics (R. Wald)] Also standard text book, but I feel it might be only the third choice for you

If you want to pursue afterwards you can have a look at DeWitt's work (however you have to get used to his style, afterwards its great)

  • Quantum field theory in curved spacetime (DeWitt)

Summarizing I would say, for an answer to the first three issues Parker & Toms or DeWitt would be the best choice, however for a general introduction Birrel & Davies is quite nice and sufficient.

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