ADVANCED CLASSICAL FIELD THEORY

Book info: ADVANCED CLASSICAL FIELD THEORY (Hardcover, 392 pages) – World Scientific Publishing Company, 2010. Language: English.

Contemporary quantum field theory is mainly developed as quantization of classical fields. Therefore, classical field theory and its BRST extension is the necessary step towards quantum field theory. This book aims to provide a complete mathematical foundation of Lagrangian classical field theory and its BRST extension for the purpose of quantization. Based on the standard geometric formulation of theory of nonlinear differential operators, Lagrangian field theory is treated in a very general setting. Reducible degenerate Lagrangian theories of even and odd fields on an arbitrary smooth manifold are considered. The second Noether theorems generalized to these theories and formulated in the homology terms provide the strict mathematical formulation of BRST extended classical field theory. The most physically relevant field theories -- gauge theory on principal bundles, gravitation theory on natural bundles, theory of spinor fields and topological field theory -- are presented in a complete way.This book is designed for theoreticians and mathematical physicists specializing in field theory. The authors have tried throughout to provide the necessary mathematical background, thus making the exposition self-contained. Editorial Reviews Review This book provides interesting insights into some of the rich geometry underpinning field theory for those already familiar with the classical theory from a more conventional standpoint. --Zentralblatt MATH

This book provides interesting insights into some of the rich geometry underpinning field theory for those already familiar with the classical theory from a more conventional standpoint. --Zentralblatt MATH

This is a very interesting book which contains a wealth of information regarding the mathematics underlying classical field theories. --Mathematical Reviews