Non-Perturbative Field Theory
From Two Dimensional Conformal Field Theory to QCD in Four Dimensions

Pedagogical exposition providing a new perspective on relativistic quantum field theory for graduate students and researchers.

Yitzhak Frishman (Author), Jacob Sonnenschein (Author)

9781107424715, Cambridge University Press

Paperback, published 10 July 2014

456 pages
24.4 x 17 x 2.3 cm, 0.72 kg

'… Non-Perturbative Field Theory will have enduring value as a comprehensive reference.' Contemporary Physics

Providing a new perspective on quantum field theory, this book gives a pedagogical and up-to-date exposition of non-perturbative methods in relativistic quantum field theory and introduces the reader to modern research work in theoretical physics. It describes in detail non-perturbative methods in quantum field theory, and explores two- dimensional and four- dimensional gauge dynamics using those methods. 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 (QCD) in particular, are thoroughly described.

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: Mathematical physics [PHU], Particle & high-energy physics [PHP], Nuclear physics [PHN]