Advanced Classical Field Theory

Front Cover
World Scientific, 2009 - Science - 392 pages
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 OCo gauge theory on principal bundles, gravitation theory on natural bundles, theory of spinor fields and topological field theory OCo 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.
 

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Contents

Introduction
1
1 Differential calculus on fibre bundles
5
2 Lagrangian field theory on fibre bundles
61
3 Grassmanngraded Lagrangian field theory
99
4 Lagrangian BRST theory
129
5 Gauge theory on principal bundles
165
6 Gravitation theory on natural bundles
215
7 Spinor fields
243
8 Topological field theories
263
9 Covariant Hamiltonian field theory
293
10 Appendixes
319
Bibliography
359
Index
369
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