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Table of Contents
Intro
Preface to the Sixth Edition
Preface to the First Edition
Contents
1 Introduction
2 The Action Principles in Mechanics
3 The Action Principle in Classical Electrodynamics
4 Application of the Action Principles
5 Jacobi Fields, Conjugate Points
6 Canonical Transformations
7 The Hamilton-Jacobi Equation
8 Action-Angle Variables
9 The Adiabatic Invariance of the Action Variables
10 Time-Independent Canonical Perturbation Theory
11 Canonical Perturbation Theory with Several Degrees of Freedom
12 Canonical Adiabatic Theory
13 Removal of Resonances
14 Superconvergent Perturbation Theory, KAM Theorem (Introduction)
15 Poincaré Surface of Sections, Mappings
16 The KAM Theorem
17 Fundamental Principles of Quantum Mechanics
18 Functional Derivative Approach
19 Examples for Calculating Path Integrals
20 Direct Evaluation of Path Integrals
21 Linear Oscillator with Time-Dependent Frequency
22 Propagators for Particles in an External Magnetic Field
23 Simple Applications of Propagator Functions
24 The WKB Approximation
25 Computing the Trace
38 The Usefulness of Lie Brackets: From Classical and Quantum Mechanics to Quantum Electrodynamics
39 Green's Function of a Spin- eepic12 Particle in a Constant External Magnetic Field
40 One-Loop Effective Lagrangian in QED
41 On Riemann's Ideas on Space and Schwinger's Treatment of Low-Energy Pion-Nucleon Physics
Riemann's Unit Sphere S2
Riemann's Unit Sphere Sn
Derivation of Riemann's Main Formula for ds2
Calculation of Riemann's Curvature Tensor, Ricci Scalar, etc.
Maximally Symmetric Metric
Realization of Chiral Symmetry in a Curved Isospin Space
Preface to the Sixth Edition
Preface to the First Edition
Contents
1 Introduction
2 The Action Principles in Mechanics
3 The Action Principle in Classical Electrodynamics
4 Application of the Action Principles
5 Jacobi Fields, Conjugate Points
6 Canonical Transformations
7 The Hamilton-Jacobi Equation
8 Action-Angle Variables
9 The Adiabatic Invariance of the Action Variables
10 Time-Independent Canonical Perturbation Theory
11 Canonical Perturbation Theory with Several Degrees of Freedom
12 Canonical Adiabatic Theory
13 Removal of Resonances
14 Superconvergent Perturbation Theory, KAM Theorem (Introduction)
15 Poincaré Surface of Sections, Mappings
16 The KAM Theorem
17 Fundamental Principles of Quantum Mechanics
18 Functional Derivative Approach
19 Examples for Calculating Path Integrals
20 Direct Evaluation of Path Integrals
21 Linear Oscillator with Time-Dependent Frequency
22 Propagators for Particles in an External Magnetic Field
23 Simple Applications of Propagator Functions
24 The WKB Approximation
25 Computing the Trace
38 The Usefulness of Lie Brackets: From Classical and Quantum Mechanics to Quantum Electrodynamics
39 Green's Function of a Spin- eepic12 Particle in a Constant External Magnetic Field
40 One-Loop Effective Lagrangian in QED
41 On Riemann's Ideas on Space and Schwinger's Treatment of Low-Energy Pion-Nucleon Physics
Riemann's Unit Sphere S2
Riemann's Unit Sphere Sn
Derivation of Riemann's Main Formula for ds2
Calculation of Riemann's Curvature Tensor, Ricci Scalar, etc.
Maximally Symmetric Metric
Realization of Chiral Symmetry in a Curved Isospin Space