Advanced Classical Field Theory

Advanced Classical Field Theory

by Benqi Guo, Luigi Mangiarotti
     
 

ISBN-10: 9812838953

ISBN-13: 9789812838957

Pub. Date: 01/28/2010

Publisher: World Scientific Publishing Company, Incorporated

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…  See more details below

Overview

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.

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Product Details

ISBN-13:
9789812838957
Publisher:
World Scientific Publishing Company, Incorporated
Publication date:
01/28/2010
Pages:
392
Product dimensions:
6.20(w) x 9.10(h) x 1.00(d)

Table of Contents

Introduction 1

1 Differential calculus on fibre bundles 5

2 Lagrangian field theory on fibre bundles 61

3 Grassmann-graded 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 Appendices 319

Bibliography 359

Index 369

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