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Does there exist a book, lecture notes, or a collection of problem sets, that contains a big number of problems in path integration technique, with solutions, akin to books that contain multitudes of exercises in calculus? Exercises in the books on QFT that I've seen, like "Quantum Field Theory" by Srednicki, "Introduction to Quantum Field Theory" by Peskin and Schroeder, or "Introduction to the Quantum Theory of Gauge Fields" by Slavnov and Faddeev, are dispersed, and usually solutions to them are not provided. "Path Integrals" by Hagen Kleinert, despite being more than 1500 pages long, does not apper to contain exercises at all, aside from occasional recommendations to the reader in the text.

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  • $\begingroup$ +1 for a question that's clear on not only what is sought, but also how nontrivial an ask it turns out to be. $\endgroup$
    – J.G.
    Commented Jan 23 at 22:18
  • $\begingroup$ Do you specifically need these problems to be about path integrals or could they also be about functional integrals? $\endgroup$
    – flippiefanus
    Commented Jan 24 at 3:28
  • $\begingroup$ As a physicist, I don't really understand the difference :) $\endgroup$
    – Daigaku no Baku
    Commented Jan 24 at 5:17

1 Answer 1

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  1. Jean Zinn-Justin, Path Integrals in Quantum Mechanics, Oxford University Press. This book covers a large number of topics using the path integral approach to (nonrelativistic) quantum mechanics and statistical physics. Each chapter is complemented with exercises and worked out solutions. An excellent introduction for novices in the field.

  2. Roland Rosenfelder, Path Integrals in Quantum Physics, https://arXiv.org/abs/1209.1315 . These lecture notes cover nonrelativistic quantum mechanics, many-body physics and field theory. Exercises with sketches of the solutions are included. Contains many illustrative examples. Highly recommended!

  3. Matthias Blau, Notes on (semi-) advanced quantum mechanics: the path integral approach to quantum mechanics, http://www.blau.itp.unibe.ch/Lecturenotes.html. Very useful for students who quickly want to get the basic ideas of the subject without going into details. Exercises (without solutions) are included.

  4. Riccardo Rattazzi, The Path Integral Approach to Quantum Mechanics, Lecture Notes for Quantum Mechanics IV, https://userswww.pd.infn.it/~feruglio/rattazzi.pdf. Covers the path integral formalism, functional and euclidean methods, the semiclassical approximation, instantons and the interaction with an external electromagnetic field. Good introduction for beginners, includes exercises without solutions.

  5. Jean Zinn-Justin, Quantum Field Theory and Critical Phenomena, Oxford University Press. An absolute "must" for advanced students and researchers who wish to acquire a deeper understanding of quantum field theory using the functional integral approach. Numerous exercises with "some" solutions at the end of the book. Not for beginners!

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  • $\begingroup$ Thank you, Zinn-Justin appears to be almost exactly what I wanted. The only downside is that it is about non-relativistic theory. $\endgroup$
    – Daigaku no Baku
    Commented Jan 24 at 13:27
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    $\begingroup$ Well, after having solved "all" exercises in (1) you could switch to (5) covering relativistic QFT. Challenging, but a phantastic book. Best wishes! $\endgroup$
    – Hyperon
    Commented Jan 24 at 13:36

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