Non-Perturbative Field Theory

A pedagogical exposition of non-perturbative methods in relativistic quantum field theory, now reissued as an Open Access title.

Yitzhak Frishman (Author), Jacob Sonnenschein (Author)

9781009401647, Cambridge University Press

Hardback, published 27 July 2023

456 pages
25.1 x 17.6 x 3.2 cm, 0.95 kg

Providing a new perspective on quantum field theory, this book gives a pedagogical exposition of non-perturbative methods in relativistic quantum field theory and introduces the reader to modern research in theoretical physics. After describing non-perturbative methods in detail, it uses these methods to explore two-dimensional and four-dimensional gauge dynamics. The book concludes with a summary emphasizing the interplay between two- and four-dimensional gauge theories. Aimed at graduate students and researchers, this book covers topics from two-dimensional conformal symmetry, affine Lie algebras, solitons, integrable models, bosonization, and 't Hooft model, to four-dimensional conformal invariance, integrability, large N expansion, Skyrme model, monopoles and instantons. Applications, first to simple field theories and gauge dynamics in two dimensions, and then to gauge theories in four dimensions and quantum chromodynamics in particular, are thoroughly described. Published originally in 2010, this title has been reissued as an Open Access publication on Cambridge Core.

Preface
Acknowledgements
Part I. Non-Perturbative Methods in Two Dimensional Field Theory: 1. From massless free scalar field to conformal field theories
2. Conformal field theory
3. Theories invariant under affine current algebras
4. Wess-Zumino-Witten model and Coset models
5. Solitons and two dimensional integrable models
6. Bosonization
7. The large N limit of two dimensional models
Part II. Two Dimensional Non-Perturbative Gauge Dynamics: 8. Gauge theories in two dimensions – basics
9. Bosonized gauge theories
10. The t'Hooft solution of 2d QCD
11. Mesonic spectrum from current algebra
12. DLCQ and the spectra of QC with fundamental and adjoint fermions
13. The baryonic spectrum of multiflavour QCD2 in the strong coupling limit
14. Confinement versus screening
15. QCD2, Coset models and BRST quantization
16. Generalized Yang Mills theory on Riemann surface
Part III. From Two to Four Dimensions: 17. Conformal invariance in four dimensional field theories and in QCD
18. Integrability in four dimensional gauge dynamics
19. Large N methods in QCD4
20. From 2d bosonized baryons to 4d skyrmions
21. From two dimensional solitons to four dimensional magnetic monopoles
22. Instantons of QCD
23. Summary, conclusions and outlook
References
Index.

Subject Areas: Statistical physics [PHS]