Preface to the First Edition Preface to the Second Edition 1.Introduction 1.1 Particles and Fields 1.2 Metric and Other Notations 1.3 Functionals 1.4 Review of Quantum Mechanics 1.5 References 2.Path Integrals and Quantum Mechanics 2.1 Basis States 2.2 Operator Ordering 2.3 The Classical Limit 2.4 Equivalence with the Schr5dinger Equation 2.5 Free Particle 2.6 References 3.Harmonic Oscillator 3.1 Path Integral for the Harmonic Oscillator 3.2 Method of Fourier Transform 3.3 Matrix Method 3.4 The Classical Action 3.5 References 4.Generating Functional 4.1 Euclidean Rotation 4.2 Time Ordered Correlation Functions 4.3 Correlation Functions in Definite States 4.4 Vacuum Functional 4.5 Anharmonic Oscillator 4.6 References 5.Path Integrals for Fermions 5.1 Fermionic Oscillator 5.2 Grassmann Variables 5.3 Generating Functional 5.4 Feynman Propagator 5.5 The Fermion Determinant 5.6 References 6.Supersymmetry 6.1 Supersymmetric Oscillator 6.2 Supersymmetric Quantum Mechanics 6.3 Shape Invariance 6.4 Example 6.5 Supersymmetry and Singular Potentials 6.5.1 Regularized Superpotential 6.5.2 Alternate Regularization 6.6 References 7.Semi-Classical Methods 7.1 WKB Approximation 7.2 Saddle Point Method 7.3 Semi-Classical Methods in Path Integrals 7.4 Double Well Potential 7.5 References
8.Path Integral for the Double Well 8.1 Instantons 8.2 Zero Modes 8.3 The Instanton Integral 8.4 Evaluating the Determinant 8.5 Multi-Instanton Contributions 8.6 References 9.Path Integral for Relativistic Theories 9.1 Systems with Many Degrees of Freedom 9.2 Relativistic Scalar Field Theory 9.3 Feynman Rules 9.4 Connected Diagrams 9.5 References 10.Effective Action 10.1 The Classical Field 10.2 Effective Action 10.3 Loop Expansion 10.4 Effective Potential at One Loop 10.5 References 11.Invarianees and Their Consequences 11.1 Symmetries of the Action 11.2 Noether's Theorem 11.2.1 Example 11.3 Complex Scalar Field 11.4 Ward Identities 11.5 Spontaneous Symmetry Breaking 11.6 Goldstone Theorem 11.7 References 12.Gauge Theories 12.1 Maxwell Theory 12.2 Non-Abelian Gauge Theory 12.3 Path Integral for Gauge Theories 12.4 BRST Invariance 12.5 Ward Identities 12.6 References 13.Anomalies 13.1 Anomalous Ward Identity 13.2 Schwinger Model 13.3 References 14.Systems at Finite Temperature 14.1 Statistical Mechanics 14.2 Critical Exponents 14.3 Harmonic Oscillator 14.4 Fermionic Oscillator 14.5 References 15.Ising Model 15.1 One Dimensional Ising Model 15.2 The Partition Function 15.3 Two Dimensional Ising Model 15.4 Duality
15.5 High and Low Temperature Expansions 15.6 Quantum Mechanical Model 15.7 Duality in the Quantum System 15.8 References Index
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