Path Integral Approach to Quantum Physics

An Introduction

Häftad, Engelska, 1996

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The present text is designed to introduce graduate students to the functional integration method in contemporary physics as painlessly as possible. The author concentrates on the conceptual problems inherent in the path integral formalism. The striking interplay between stochastic processes, statistical physics and quantum mechanics comes to the fore. The reader will find all the methods of fundamental interest amply illustrated by important physical examples.

Produktinformation

Utgivningsdatum1996-06-20
Mått155 x 235 x 22 mm
Vikt610 g
FormatHäftad
SpråkEngelska
SerieTheoretical and Mathematical Physics
Antal sidor387
FörlagSpringer-Verlag Berlin and Heidelberg GmbH & Co. KG
ISBN9783540611066

Tillhör följande kategorier

Fysik inom Naturvetenskap och teknik
Matematisk statistik inom Naturvetenskap och teknik
Kvantfysik inom Naturvetenskap och teknik
Matematisk fysik inom Naturvetenskap och teknik

1. Brownian Motion.- 1.1 The One-Dimensional Random Walk.- 1.2 Multidimensional Random Walk.- 1.3 Generating Functions.- 1.4 The Continuum Limit.- 1.5 Imaginary Time.- 1.6 The Wiener Process.- 1.7 Expectation Values.- 1.8 The Ornstein-Uhlenbeck Process.- 2. The Feynman-Kac Formula.- 2.1 The Conditional Wiener Measure.- 2.2 The Integral Equation Method.- 2.3 The Lie-Trotter Product Method.- 2.4 The Brownian Tube.- 2.5 The Golden-Thompson-Symanzik Bound.- 2.6 Hamiltonians and Their Associated Processes.- 2.7 The Thermodynamical Formalism.- 2.8 A Case Study: the Harmonic Spin Chain.- 2.9 The Reflection Principle.- 2.10 Feynman Versus Wiener Integrals.- 3. The Brownian Bridge.- 3.1 The Canonical Scaling of Brownian Paths.- 3.2 Bounds on the Transition Amplitude.- 3.3 Variational Principles.- 3.4 Bound States.- 3.5 Monte Carlo Calculation of Path Integrals.- 4. Fourier Decomposition.- 4.1 Random Fourier Coefficients.- 4.2 The Wigner-Kirkwood Expansion of the Effective Potential.- 4.3 Coupled Systems.- 4.4 The Driven Harmonic Oscillator.- 4.5 Oscillating Electric Fields.- 5. The Linear-Coupling Theory of Bosons.- 5.1 Path Integrals for Bosons.- 5.2 A Random Potential for the Electron.- 5.3 The Polaron Problem.- 5.4 The Field Theory of the Polaron Model.- 6. Magnetic Fields.- 6.1 Heuristic Considerations.- 6.2 Itô Integrals.- 6.3 The Constant Magnetic Field.- 6.4 Diamagnetism of Electrons in a Solid.- 6.5 Magnetic Flux Lines.- 7. Euclidean Field Theory.- 7.1 What Is a Euclidean Field?.- 7.2 The Euclidean Two-Point Function.- 7.3 The Euclidean Free Field.- 7.4 Gaussian Functional Integrals.- 7.5 Basic Postulates.- 8. Field Theory on a Lattice.- 8.1 The Lattice Version of the Scalar Field.- 8.2 The Euclidean Propagator on the Lattice.- 8.3 The Variational Principle.- 8.4 TheEffective Action.- 8.5 The Effective Potential.- 8.6 The Ginzburg-Landau Equations.- 8.7 The Mean-Field Approximation.- 8.8 The Gaussian Approximation.- 9. The Quantization of Gauge Theories.- 9.1 The Euclidean Version of Maxwell Theory.- 9.2 Non-Abelian Gauge Theories: Preliminaries.- 9.3 The Faddeev-Popov Quantization.- 9.4 Gauge Theories on a Lattice.- 9.5 Wegner-Wilson Loops.- 9.6 The SU(n) Higgs Model.- 10. Fermions.- 10.1 The Dirac Field in Minkowski Space.- 10.2 The Euclidean Dirac Field.- 10.3 Grassmann Algebras.- 10.4 Formal Derivatives.- 10.5 Formal Integration.- 10.6 Functional Integrals of QED.- 10.7 The SU(n) Gauge Theory with Fermions.- Appendices.- A List of Symbols and Glossary.- B Frequently Used Gaussian Processes.- C Jensen’s Inequality.- D A Table of Path Integrals.- References.