Books on non-perturbative phenomena in quantum field theory

Question

I am looking for any good places (preferably textbooks) to study about introductory non-perturbative phenomena in Quantum field theory.
Any suggestion will be appreciated.

Answer 1

The following books assume some acquaintance with perturbative quantum field theory. Together they cover a very wide spectrum of nonperturbative techniques for very different situations.

• E. Calzetta and B. Hu. Nonequilibrium Quantum Field Theory. Cambridge Univ. Press (2008). A book on nonperturbative quantum field theory at finite time and finite temperature.

• Y. Frishman and J. Sonnenschein. Non-Perturbative Field Theory. Cambridge Univ. Press (2010). A book on nonperturbative quantum field theory with emphasis on 2-dimensional exactly solvable models.

• M. Shifman. Advanced Topics in Quantum Field Theory. Cambridge Univ. Press (2012). A book on nonperturbative quantum field theory with emphasis on supersymmetry.

Answer 2

If you're interested in non-perturbative aspects of quantum field theory, you should study lattice quantum field theory. In fact, you'd be negligent not to: Lattice QFT is the only reasonably general way of defining non-perturbative quantum field theory, and frequently the only practical way of doing concrete non-perturbative computations. It's also pedagogically worthwhile: Because lattice QFT is oriented towards non-perturbative phenomena, its textbooks present QFT without the usual perturbative haze. You get a much cleaner view of what QFT is.

Decent textbooks include:

• Smit, Introduction to Quantum Fields on a Lattice
• Montvay, Muster, Quantum Fields on a Lattice

I also like the following notes:

• LePage, Lattice QCD for Novices, https://arxiv.org/abs/hep-lat/0506036
• McGreevy, Whence QFT?, found at https://mcgreevy.physics.ucsd.edu/s14/

You should also take some time to study Conformal Field Theory, which is usually concerned with phenomena inaccessible to perturbation theory. There're a number of standard textbooks & lectures notes. For brevity, I'll mention:

• di Francesco et al, Conformal Field Theory (the bible of 2d CFT)
• Rychkov, EPFL Lectures on Conformal Field Theory in D>= 3 Dimensions, https://arxiv.org/abs/1601.05000

Lastly, you should spend some time learning about topological aspects of non-perturbative QFT, meaning anomalies, instantons & such.

• Coleman, Aspects of Symmetry, (the classic introduction, but not much on anomalies)
• Polyakov, Gauge fields and strings, (eclectic and interesting)
• Bilal, Lectures on Anomalies, (solid & modern)

Answer 3

The OP did not explain what "nonperturbative" means, which can vary. So I will go with beyond perturbation theory, i.e., not just talking of correlations of a QFT as formal power series in $\hbar$ or the renormalized coupling constant. In that case, the literature on constructive quantum field theory deserves to be mentioned (although it might be too mathematical for OP's taste).

The classical reference is the book by Glimm and Jaffe "Quantum Physics: A Functional Integral Point of View". It starts from classical mechanics and statistical mechanics and goes through QM and finally QFT. Not an easy read but it is quite thorough and mathematically rigorous.

Another reference is the book "From Perturbative to Constructive Renormalization" by Rivasseau which is more technical and is a better source for topics like cluster expansions.

Answer 4

For an essentially introductory, well illustrated (!) QFT book for the future, one might do worse than taking a look at Yannick Meurice's

• Quantum Field Theory: A Quantum Computation Approach (April 2021) (IOP Expanding Physics, IOP Publishing Ltd) ISBN-13 : 978-0750321853

Rather than getting students up to speed for cranking out perturbative cross sections, it dares to bridge the gap to computational physics simulations in finite (small) Hilbert spaces, instead. Focuses on lattice simulation experiments for strongly interacting systems, expressly poised to utilize quantum computing--"an ineluctable modality of the visible (Joyce)", in the author's vision.