Non-perturbative field theory
Subtitle: from two dimensional conformal field theory to QCD in four dimensions
By: Yitzhak Frishman, Jacob Sonnenschein.
Contributors: Sonnenschein, Jacob.
Series: Cambridge monographs on mathematical physics
Publisher: Cambridge University Press
Published: 2009
Place of publication: New York
Language: eng
ISBN-13: 9780521662659
Subjects: Field theory (Physics); Perturbation (Quantum dynamics)
Description: "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"--Provided by publisher.

"Field theory is the framework with which one describes the theory of the standard model of elementary particles and their interactions. The electromagnetic sector (QED) of the standard model is understood extremely well using perturbation theory, but the color interaction (QCD) which is responsible for hadron physics can only be accounted for perturbatively for a limited set of observational data. Due to the fact that at long distances the color interaction is strongly coupled, one cannot reliably apply perturbative methods to extract, for instance, the spectrum of the hadrons. The arsenal of tools to handle strongly coupled systems is obviously much more limited than the one used for weakly coupled ones. Nevertheless, several methods to handle non-perturbative field theories have been developed. The main goal of this book is to expose the reader to those techniques and to describe their applications in two-dimensional and four-dimensional field theories and finally in QCD in four dimensions"--Provided by publisher.
Notes: Includes bibliographical references and index.
Table of contents: title: Machine generated contents note: 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.