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《簡明量子場論》內容簡介:As a student, I was rearing at the bit, after a course on quantum mechanics, tolearn quantum field theory, but the books on the subject all seemed so formidable.Fortunately, I came across a little book by Mandl on field theory, which gaveme a taste of the subject enabling me to go on and tackle the more substantivetexts. I have since learned that other physicists of my generation had similar goodexperiences with Mandl.
目次
Preface
Convention, Notation, and Units
PART Ⅰ MOTIVATION AND FOUNDATION
Ⅰ.1 Who Needs It?
Ⅰ.2 Path Integral Formulation of Quantum Physics
Ⅰ.3 From Mattress to Field
Ⅰ.4 From Field to Particle to Force
Ⅰ.5 Coulomb and Newton: Repulsion and Attraction
Ⅰ.6 Inverse Square Law and the Floating 3-Brane
Ⅰ.7 Feynman Diagrams
Ⅰ.8 Quantizing Canonically and Disturbing the Vacuum
Ⅰ.9 Symmetry
Ⅰ.10 Field Theory in Curved Spacetime
Ⅰ.11 Field Theory Redux
PART Ⅱ DIRAC AND THE SPINOR
Ⅱ.1 The Dirac Equation
Ⅱ.2 Quantizing the Dirac Field
Ⅱ.3 Lorentz Group and Weyl Spinors
Ⅱ.4 Spin-Statistics Connection
Ⅱ.5 Vacuum Energy, Grassmann Integrals, and Feynman Diagrams for Fermions
Ⅱ.6 Electron Scattering and Gauge Invariance
Ⅱ.7 Diagrammatic Proof of Gauge Invariance
PART Ⅲ RENORMALIZATION AND GAUGE INVARIANCE
Ⅲ.1 Cutting Off Our Ignorance
Ⅲ.2 Renormalizable versus Nonrenormalizable
Ⅲ.3 Counterterms and Physical Perturbation Theory
Ⅲ.4 Gauge Invariance: A Photon Can Find No Rest
Ⅲ.5 Field Theory without Relativity
Ⅲ.6 The Magnetic Moment of the Electron
Ⅲ.7 Polarizing the Vacuum and Renormalizing the Charge
PART Ⅳ SYMMETRY AND SYMMETRY BREAKING
Ⅳ.1 Symmetry Breaking
Ⅳ.2 The Pion as a Nambu-Goldstone Boson
Ⅳ.3 Effective Potential
Ⅳ.4 Magnetic Monopole
Ⅳ.5 Nonabelian Gauge Theory
Ⅳ.6 The Anderson-Higgs Mechanism
Ⅳ.7 Chiral Anomaly
PART Ⅴ FIELD THEORY AND COLLECTIVE PHENOMENA
Ⅴ.1 Superfluids
Ⅴ.2 Euclid, Boltzmann, Hawking, and Field Theory at Finite Temperature
Ⅴ.3 Landau-Ginzburg Theory of Critical Phenomena
Ⅴ.4 Superconductivity
Ⅴ.5 Peierls Instability
Ⅴ.6 Solitons
Ⅴ.7 Vortices, Monopoles, and Instantons
PART Ⅵ FIELD THEORY AND CONDENSED MATTER
Fractional Statistics, Chem-Simons Term, and Topological
Field Theory
Quantum Hall Fluids
Duality
The δ Models as Effective Field Theories
Ferromagnets and Antiferromagnets
Surface Growth and Field Theory
Disorder: Replicas and Grassmannian Symmetry
Renormalization Group Flow as a Natural Concept in
High Energy and Condensed Matter Physics
PART Ⅶ GRAND UNIFICATION
Quantizing Yang-Mills Theory and Lattice Gauge Theory .
Electroweak Unification
Quantum Chromodynamics
Large N Expansion
Grand Unification
Protons Are Not Forever
SO(10) Unification
PART Ⅷ GRAVITY AND BEYOND
Gravity as a Field Theory and the Kaluza-Klein Picture
The Cosmological Constant Problem and the Cosmic
Coincidence Problem
Effective Field Theory Approach to Understanding Nature .
Supersymmetry: A Very Brief Introduction
A Glimpse of String Theory as a 2-Dimensional
Field Theory
Closing Words
APPENDIXES
A Gaussian Integration and the Central Identity of Quantum Field Theory
B A Brief Review of Group Theory
C Feynman Rules
D Various Identities and Feynman Integrals
E Dotted and Undotted Indices and the Majorana Spinor Solutions to Selected Exercises
Further Reading
Index
Convention, Notation, and Units
PART Ⅰ MOTIVATION AND FOUNDATION
Ⅰ.1 Who Needs It?
Ⅰ.2 Path Integral Formulation of Quantum Physics
Ⅰ.3 From Mattress to Field
Ⅰ.4 From Field to Particle to Force
Ⅰ.5 Coulomb and Newton: Repulsion and Attraction
Ⅰ.6 Inverse Square Law and the Floating 3-Brane
Ⅰ.7 Feynman Diagrams
Ⅰ.8 Quantizing Canonically and Disturbing the Vacuum
Ⅰ.9 Symmetry
Ⅰ.10 Field Theory in Curved Spacetime
Ⅰ.11 Field Theory Redux
PART Ⅱ DIRAC AND THE SPINOR
Ⅱ.1 The Dirac Equation
Ⅱ.2 Quantizing the Dirac Field
Ⅱ.3 Lorentz Group and Weyl Spinors
Ⅱ.4 Spin-Statistics Connection
Ⅱ.5 Vacuum Energy, Grassmann Integrals, and Feynman Diagrams for Fermions
Ⅱ.6 Electron Scattering and Gauge Invariance
Ⅱ.7 Diagrammatic Proof of Gauge Invariance
PART Ⅲ RENORMALIZATION AND GAUGE INVARIANCE
Ⅲ.1 Cutting Off Our Ignorance
Ⅲ.2 Renormalizable versus Nonrenormalizable
Ⅲ.3 Counterterms and Physical Perturbation Theory
Ⅲ.4 Gauge Invariance: A Photon Can Find No Rest
Ⅲ.5 Field Theory without Relativity
Ⅲ.6 The Magnetic Moment of the Electron
Ⅲ.7 Polarizing the Vacuum and Renormalizing the Charge
PART Ⅳ SYMMETRY AND SYMMETRY BREAKING
Ⅳ.1 Symmetry Breaking
Ⅳ.2 The Pion as a Nambu-Goldstone Boson
Ⅳ.3 Effective Potential
Ⅳ.4 Magnetic Monopole
Ⅳ.5 Nonabelian Gauge Theory
Ⅳ.6 The Anderson-Higgs Mechanism
Ⅳ.7 Chiral Anomaly
PART Ⅴ FIELD THEORY AND COLLECTIVE PHENOMENA
Ⅴ.1 Superfluids
Ⅴ.2 Euclid, Boltzmann, Hawking, and Field Theory at Finite Temperature
Ⅴ.3 Landau-Ginzburg Theory of Critical Phenomena
Ⅴ.4 Superconductivity
Ⅴ.5 Peierls Instability
Ⅴ.6 Solitons
Ⅴ.7 Vortices, Monopoles, and Instantons
PART Ⅵ FIELD THEORY AND CONDENSED MATTER
Fractional Statistics, Chem-Simons Term, and Topological
Field Theory
Quantum Hall Fluids
Duality
The δ Models as Effective Field Theories
Ferromagnets and Antiferromagnets
Surface Growth and Field Theory
Disorder: Replicas and Grassmannian Symmetry
Renormalization Group Flow as a Natural Concept in
High Energy and Condensed Matter Physics
PART Ⅶ GRAND UNIFICATION
Quantizing Yang-Mills Theory and Lattice Gauge Theory .
Electroweak Unification
Quantum Chromodynamics
Large N Expansion
Grand Unification
Protons Are Not Forever
SO(10) Unification
PART Ⅷ GRAVITY AND BEYOND
Gravity as a Field Theory and the Kaluza-Klein Picture
The Cosmological Constant Problem and the Cosmic
Coincidence Problem
Effective Field Theory Approach to Understanding Nature .
Supersymmetry: A Very Brief Introduction
A Glimpse of String Theory as a 2-Dimensional
Field Theory
Closing Words
APPENDIXES
A Gaussian Integration and the Central Identity of Quantum Field Theory
B A Brief Review of Group Theory
C Feynman Rules
D Various Identities and Feynman Integrals
E Dotted and Undotted Indices and the Majorana Spinor Solutions to Selected Exercises
Further Reading
Index
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