文档介绍：Natural and Gauge Natural Formalism for
Classical Field Theories
NATURAL AND GAUGE NATURAL
FORMALISM FOR CLASSICAL
FIELD THEORIES
A Geometric Perspective including
Spinors and Gauge Theories
LORENZO FATIBENE
MAURO FRANCAVIGLIA
Dipartimento di Matematica
University of Torino, ITALY
Kluwer Academic Publishers
Boston/Dordrecht/London
Mauro dedicates this book
to the memory of
his beloved wife Anna.
Contents
Foreword xi
Introduction xv
Acknowledgments xxi
Part I The Geometric Setting
Introduction 0
1. FIBER BUNDLES 0
1 Definition of Fiber Bundles 0
2 Fibered Coordinates 0
3 Particular Classes of Fiber Bundles 0
4 Fiber Bundles with Structure Group 0
5 Canonical Constructions of Bundles 0
6 Vector Fields on a Bundle 0
Exercises 0
2. JET BUNDLES 0
1 The Jet Bundles 0
2 Prolongation of Morphisms and Sections 0
3 Contact Forms 0
4 The Infinite Jet Bundle 0
5 Generalized Vector Fields 0
6 Lie Derivative of Sections 0
7 Examples 0
CONTENTS ix
8 Differential Equations 0
Exercises 0
3. PRINCIPAL BUNDLES AND CONNECTIONS 0
1 Principal Bundles and Their Right Action 0
2 Invariant Vector Fields 0
3 Local Expression of Principal Automorphisms 0
4 Infinitesimal Generators of Automorphisms 0
5 Bundle Connections 0
6 Induced Connections on Associated Bundles 0
7 Examples 0
8 Structures Induced by a Connection 0
Exercises 0
4. NATURAL BUNDLES 0
1 Natural Bundles 0
2 Natural Morphisms 0
3 Lie Derivatives of Sections 0
4 Examples 0
Exercises 0
5. GAUGE NATURAL BUNDLES 0
1 Gauge Natural Bundles 0
2 Gauge Natural Prolongations of a Principal Bundle 0
3 The Infinitesimal Generators of Automorphisms (IGA) 0
4 Lie Derivatives of Sections 0
5 Examples 0
Exercises 0
Part II The Variational Structure of Field Theories
Introduction 0
6. THE LAGRANGIAN FORMALISM 0
x NATURAL AND GAUGE NATURAL FORMALISM
1 The Lagrangian and the Action Functional 0
2 The Variational Morphisms 0
3 Euler-Lagrange E