Non-Perturbative Field Theory

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