Michael Stone

The Physics of Quantum Fields (eBook, PDF)

• Format: PDF

Produktbeschreibung

A gentle introduction to the physics of quantized fields and many-body physics. Based on courses taught at the University of Illinois, it concentrates on the basic conceptual issues that many students find difficult, and emphasizes the physical and visualizable aspects of the subject. While the text is intended for students with a wide range of interests, many of the examples are drawn from condensed matter physics because of the tangible character of such systems. The first part of the book uses the Hamiltonian operator language of traditional quantum mechanics to treat simple field theories and related topics, while the Feynman path integral is introduced in the second half where it is seen as indispensable for understanding the connection between renormalization and critical as well as non-perturbative phenomena.

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Produktdetails

• Verlag: Springer US
• Seitenzahl: 271
• Erscheinungstermin: 6. Dezember 2012
• Englisch
• ISBN-13: 9781461205074
• Artikelnr.: 44043525

Inhaltsangabe

1 Discrete Systems.- 1.1 One-Dimensional Harmonic Crystal.- 1.2 Continuum Limit.- 2 Relativistic Scalar Fields.- 2.1 Conventions.- 2.2 The Klein-Gordon Equation.- 2.3 Symmetries and Noether's Theorem.- 3 Perturbation Theory.- 3.1 Interactions.- 3.2 Perturbation Theory.- 3.3 Wick's Theorem.- 4 Feynman Rules.- 4.1 Diagrams.- 4.2 Scattering Theory.- 5 Loops, Unitarity, and Analyticity.- 5.1 Unitarity of the S Matrix.- 5.2 The Analytic S Matrix.- 5.3 Some Loop Diagrams.- 6 Formal Developments.- 6.1 Gell-Mann Low Theorem.- 6.2 Lehmann-Källén Spectral Representation.- 6.3 LSZ Reduction Formulae.- 7 Fermions.- 7.1 Dirac Equation.- 7.2 Spinors, Tensors, and Currents.- 7.3 Holes and the Dirac Sea.- 7.4 Quantization.- 8 QED.- 8.1 Quantizing Maxwell's Equations.- 8.2 Feynman Rules for QED.- 8.3 Ward Identity and Gauge Invariance.- 9 Electrons in Solids.- 9.1 Second Quantization.- 9.2 Fermi Gas and Fermi Liquid.- 9.3 Electrons and Phonons.- 10 Nonrelativistic Bosons.- 10.1 The Boson Field.- 10.2 Spontaneous Symmetry Breaking.- 10.3 Dilute Bose Gas.- 10.4 Charged Bosons.- 11 Finite Temperature.- 11.1 Partition Functions.- 11.2 Worldlines.- 11.3 Matsubara Sums.- 12 Path Integrals.- 12.1 Quantum Mechanics of a Particle.- 12.2 Gauge Invariance and Operator Ordering.- 12.3 Correlation Functions.- 12.4 Fields.- 12.5 Gaussian Integrals and Free Fields.- 12.6 Perturbation Theory.- 13 Functional Methods.- 13.1 Generating Functionals.- 13.2 Ward Identities.- 14 Path Integrals for Fermions.- 14.1 Berezin Integrals.- 14.2 Fermionic Coherent States.- 14.3 Superconductors.- 15 Lattice Field Theory.- 15.1 Boson Fields.- 15.2 Random Walks.- 15.3 Interactions and Bose Condensation.- 15.4 Lattice Fermions.- 16 The Renormalization Group.- 16.1 Transfer Matrices.- 16.2 Block Spins and Renormalization Group.- 17 Fields and Renormalization.- 17.1 The Free-Field Fixed Point.- 17.2 The Gaussian Model.- 17.3 General Method.- 17.4 Nonlinear ? Model.- 17.5 Renormalizing ??4.- 18 Large N Expansions.- 18.1O(N) Linear ?-Model.- 18.2 Large N Expansions.- A Relativistic State Normalization.- B The General Commutator.- C Dimensional Regularization.- C.1 Analytic Continuation and Integrals.- C.2 Propagators.- D Spinors and the Principle of the Sextant.- D.1 Constructing the ?-Matrices.- D.2 Basic Theorem.- D.3 Chirality.- E Indefinite Metric.- F Phonons and Momentum.- G Determinants in Quantum Mechanics.