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Introduction to Quantum Field Theory: Classical Mechanics to Gauge Field Theories [Kõva köide]

4.50/5 (4 hinnangut Goodreads-ist)
(University of Adelaide)
  • Formaat: Hardback, 792 pages, kõrgus x laius x paksus: 261x208x39 mm, kaal: 2020 g, Worked examples or Exercises
  • Ilmumisaeg: 04-Aug-2022
  • Kirjastus: Cambridge University Press
  • ISBN-10: 1108470904
  • ISBN-13: 9781108470902
Teised raamatud teemal:
Introduction to Quantum Field Theory: Classical Mechanics to Gauge Field TheoriesSuurem pilt
  • Formaat: Hardback, 792 pages, kõrgus x laius x paksus: 261x208x39 mm, kaal: 2020 g, Worked examples or Exercises
  • Ilmumisaeg: 04-Aug-2022
  • Kirjastus: Cambridge University Press
  • ISBN-10: 1108470904
  • ISBN-13: 9781108470902
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9781108470902.html
Märksõnad:
"This textbook offers a detailed and uniquely self-contained presentation of quantum and gauge field theories. Writing from a modern perspective, the author begins with a discussion of advanced dynamics and special relativity before guiding students steadily through the fundamental principles of relativistic quantum mechanics and classical field theory. This foundation is then used to develop the full theoretical framework of quantum and gauge field theories. The introductory, opening half of the book allows it to be used for a variety of courses, from advanced undergraduate to graduate level, and students lacking a formal background in more elementary topics will benefit greatly from this approach. Williams provides full derivations wherever possible and adopts a pedagogical tone without sacrificing rigor. Worked examples are included throughout the text and end-of-chapter problems help students to reinforce key concepts. A fully worked solutions manual is available online for instructors"--

Arvustused

'This new and very welcome introduction to quantum field theory takes the reader from the basics of classical physics and the beauty of group theory to the intricacies and elegance of gauge field theories. Students and researchers alike will treasure this fresh approach to one of the foundation stones of modern physics.' Thomas Appelquist, Yale University 'I wish this text had been available the last time I taught quantum field theory. The author provides clear, detailed expositions, which serve students with diverse backgrounds for multiple course syllabi.' Steve Gottlieb, Indiana University 'The rigorous and logical approach makes this text certainly one to be seriously considered for use in a quantum field theory course. In any case, it is one which practitioners will definitely want to have within easy reach on their bookshelf.' Barry Holstein, University of Massachusetts Amherst 'Both as an introductory text and as an excellent single-volume compendium on quantum field theory, this book is highly recommended for students as well as practitioners at all levels.' Wolfram Weise, Technical University of Munich

Muu info

This detailed and self-contained presentation of quantum field theory is suitable for advanced undergraduate and graduate level courses.
Preface xv
Organization of the Book xvi
How to Use This Book xvii
Acknowledgments xviii
1 Lorentz and Poincare Invariance
1(56)
1.1 Introduction
1(3)
1.1.1 Inertial Reference Frames
1(1)
1.1.2 Galilean Relativity
2(2)
1.2 Lorentz and Poincare Transformations
4(41)
1.2.1 Postulates of Special Relativity and Their Implications
4(8)
1.2.2 Active and Passive Transformations
12(2)
1.2.3 Lorentz Group
14(22)
1.2.4 Poincare Group
36(4)
1.2.5 Representation-Independent Poincare Lie Algebra
40(5)
1.3 Representations of the Lorentz Group
45(2)
1.3.1 Labeling Representations of the Lorentz Group
45(1)
1.3.2 Lorentz Transformations of Weyl Spinors
46(1)
1.4 Poincare Group and the Little Group
47(10)
1.4.1 Intrinsic Spin and the Poincare Group
47(1)
1.4.2 The Little Group
48(5)
Summary
53(1)
Problems
54(3)
2 Classical Mechanics
57(99)
2.1 Lagrangian Formulation
57(12)
2.1.1 Euler-Lagrange Equations
58(6)
2.1.2 Hamilton's Principle
64(3)
2.1.3 Lagrange Multipliers and Constraints
67(2)
2.2 Symmetries, Noether's Theorem and Conservation Laws
69(4)
2.3 Small Oscillations and Normal Modes
73(5)
2.4 Hamiltonian Formulation
78(10)
2.4.1 Hamiltonian and Hamilton's Equations
78(2)
2.4.2 Poisson Brackets
80(4)
2.4.3 Liouville Equation and Liouville's Theorem
84(1)
2.4.4 Canonical Transformations
85(3)
2.5 Relation to Quantum Mechanics
88(7)
2.6 Relativistic Kinematics
95(4)
2.7 Electromagnetism
99(18)
2.7.1 Maxwell's Equations
99(6)
2.7.2 Electromagnetic Waves
105(4)
2.7.3 Gauge Transformations and Gauge Fixing
109(8)
2.8 Analytic Relativistic Mechanics
117(9)
2.9 Constrained Hamiltonian Systems
126(30)
2.9.1 Construction of the Hamiltonian Approach
126(18)
2.9.2 Summary of the Dirac-Bergmann Algorithm
144(4)
2.9.3 Gauge Fixing, the Dirac Bracket and Quantization
148(2)
2.9.4 Dirac Bracket and Canonical Quantization
150(2)
Summary
152(1)
Problems
152(4)
3 Relativistic Classical Fields
156(49)
3.1 Relativistic Classical Scalar Fields
156(10)
3.2 Noether's Theorem and Symmetries
166(19)
3.2.1 Noether's Theorem for Classical Fields
166(8)
3.2.2 Stress-Energy Tensor
174(2)
3.2.3 Angular Momentum Tensor
176(3)
3.2.4 Intrinsic Angular Momentum
179(2)
3.2.5 Internal Symmetries
181(1)
3.2.6 Belinfante-Rosenfeld Tensor
182(1)
3.2.7 Noether's Theorem and Poisson Brackets
183(1)
3.2.8 Generators of the Poincare Group
184(1)
3.3 Classical Electromagnetic Field
185(20)
3.3.1 Lagrangian Formulation of Electromagnetism
185(3)
3.3.2 Hamiltonian Formulation of Electromagnetism
188(13)
Summary
201(1)
Problems
202(3)
4 Relativistic Quantum Mechanics
205(110)
4.1 Review of Quantum Mechanics
205(43)
4.1.1 Postulates of Quantum Mechanics
205(7)
4.1.2 Notation, Linear and Antilinear Operators
212(3)
4.1.3 Symmetry Transformations and Wigner's Theorem
215(1)
4.1.4 Projective Representations of Symmetry Groups
216(5)
4.1.5 Symmetry in Quantum Systems
221(1)
4.1.6 Parity Operator
222(1)
4.1.7 Time Reversal Operator
223(6)
4.1.8 Additive and Multiplicative Quantum Numbers
229(3)
4.1.9 Systems of Identical Particles and Fock Space
232(4)
4.1.10 Charge Conjugation and Antiparticles
236(3)
4.1.11 Interaction Picture in Quantum Mechanics
239(2)
4.1.12 Path Integrals in Quantum Mechanics
241(7)
4.2 Wavepackets and Dispersion
248(6)
4.3 Klein-Gordon Equation
254(10)
4.3.1 Formulation of the Klein-Gordon Equation
254(3)
4.3.2 Conserved Current
257(3)
4.3.3 Interaction with a Scalar Potential
260(2)
4.3.4 Interaction with an Electromagnetic Field
262(2)
4.4 Dirac Equation
264(25)
4.4.1 Formulation of the Dirac Equation
265(3)
4.4.2 Probability Current
268(1)
4.4.3 Nonrelativistic Limit and Relativistic Classical Limit
268(2)
4.4.4 Interaction with an Electromagnetic Field
270(4)
4.4.5 Lorentz Covariance of the Dirac Equation
274(3)
4.4.6 Dirac Adjoint Spinor
277(1)
4.4.7 Plane Wave Solutions
278(5)
4.4.8 Completeness and Projectors
283(1)
4.4.9 Spin Vector
284(2)
4.4.10 Covariant Interactions and Bilinears
286(1)
4.4.11 Poincare Group and the Dirac Equation
287(2)
4.5 P, C and T: Discrete Transformations
289(11)
4.5.1 Parity Transformation
289(2)
4.5.2 Charge Conjugation
291(4)
4.5.3 Time Reversal
295(3)
4.5.4 CPT Transformation
298(2)
4.6 Chirality and Weyl and Majorana Fermions
300(11)
4.6.1 Helicity
300(1)
4.6.2 Chirality
301(1)
4.6.3 Weyl Spinors and the Weyl Equations
302(2)
4.6.4 Plane Wave Solutions in the Chiral Representation
304(2)
4.6.5 Majorana Fermions
306(1)
4.6.6 Weyl Spinor Notation
307(4)
4.7 Additional Topics
311(4)
Summary
313(1)
Problems
313(2)
5 Introduction to Particle Physics
315(50)
5.1 Overview of Particle Physics
315(4)
5.2 The Standard Model
319(27)
5.2.1 Development of Quantum Electrodynamics (QED)
319(3)
5.2.2 Development of Quantum Chromodynamics (QCD)
322(7)
5.2.3 Development of Electroweak (EW) Theory
329(6)
5.2.4 Quark Mixing and the CKM Matrix
335(3)
5.2.5 Neutrino Mixing and the PMNS Matrix
338(6)
5.2.6 Majorana Neutrinos and Double Beta Decay
344(2)
5.3 Representations of SU(N) and the Quark Model
346(19)
5.3.1 Multiplets of SU(N) and Young Tableaux
346(12)
5.3.2 Quark Model
358(5)
Summary
363(1)
Problems
363(2)
6 Formulation of Quantum Field Theory
365(138)
6.1 Lessons from Quantum Mechanics
365(5)
6.1.1 Quantization of Normal Modes
366(4)
6.1.2 Motivation for Relativistic Quantum Field Theory
370(1)
6.2 Scalar Particles
370(47)
6.2.1 Free Scalar Field
371(11)
6.2.2 Field Configuration and Momentum Density Space
382(1)
6.2.3 Covariant Operator Formulation
383(5)
6.2.4 Poincare Covariance
388(4)
6.2.5 Causality and Spacelike Separations
392(2)
6.2.6 Feynman Propagator for Scalar Particles
394(5)
6.2.7 Charged Scalar Field
399(5)
6.2.8 Wick's Theorem
404(3)
6.2.9 Functional Integral Formulation
407(5)
6.2.10 Euclidean Space Formulation
412(1)
6.2.11 Generating Functional for a Scalar Field
413(4)
6.3 Fermions
417(40)
6.3.1 Annihilation and Creation Operators
418(1)
6.3.2 Fock Space and Grassmann Algebra
419(8)
6.3.3 Feynman Path Integral for Fermions
427(1)
6.3.4 Fock Space for Dirac Fermions
428(4)
6.3.5 Functional Integral for Dirac Fermions
432(4)
6.3.6 Canonical Quantization of Dirac Fermions
436(10)
6.3.7 Quantum Field Theory for Dirac Fermions
446(7)
6.3.8 Generating Functional for Dirac Fermions
453(4)
6.4 Photons
457(27)
6.4.1 Canonical Quantization of the Electromagnetic Field
457(1)
6.4.2 Fock Space for Photons
458(8)
6.4.3 Functional Integral for Photons
466(2)
6.4.4 Gauge-Fixing
468(8)
6.4.5 Covariant Canonical Quantization for Photons
476(8)
6.5 Massive Vector Bosons
484(19)
6.5.1 Classical Massive Vector Field
485(4)
6.5.2 Normal Modes of the Massive Vector Field
489(1)
6.5.3 Quantization of the Massive Vector Field
490(4)
6.5.4 Functional Integral for Massive Vector Bosons
494(3)
6.5.5 Covariant Canonical Quantization for Massive Vector Bosons
497(1)
Summary
498(1)
Problems
499(4)
7 Interacting Quantum Field Theories
503(97)
7.1 Physical Spectrum of States
503(4)
7.2 Kallen-Lehmann Spectral Representation
507(3)
7.3 Scattering Cross-Sections and Decay Rates
510(23)
7.3.1 Cross-Section
511(9)
7.3.2 Relating the Cross-Section to the 5-Matrix
520(7)
7.3.3 Particle Decay Rates
527(1)
7.3.4 Two-Body Scattering (2 → 2) and Mandelstam Variables
528(4)
7.3.5 Unitarity of the 5-Matrix and the Optical Theorem
532(1)
7.4 Interaction Picture and Feynman Diagrams
533(13)
7.4.1 Interaction Picture
534(3)
7.4.2 Feynman Diagrams
537(7)
7.4.3 Feynman Rules in Momentum Space
544(2)
7.5 Calculating Invariant Amplitudes
546(23)
7.5.1 LSZ Reduction Formula for Scalars
546(11)
7.5.2 LSZ for Fermions
557(7)
7.5.3 LSZ for Photons
564(5)
7.6 Feynman Rules
569(31)
7.6.1 External States and Internal Lines
570(2)
7.6.2 Examples of Interacting Theories
572(6)
7.6.3 Example Tree-Level Results
578(8)
7.6.4 Substitution Rules and Crossing Symmetry
586(1)
7.6.5 Examples of Calculations of Cross-Sections
587(7)
7.6.6 Unstable Particles
594(2)
Summary
596(1)
Problems
597(3)
8 Symmetries and Renormalization
600(93)
8.1 Discrete Symmetries: P, C and T
600(25)
8.1.1 Parity
600(8)
8.1.2 Charge Conjugation
608(5)
8.1.3 Time Reversal
613(5)
8.1.4 The C/T Theorem
618(5)
8.1.5 Spin-Statistics Connection
623(2)
8.2 Generating Functionals and the Effective Action
625(8)
8.2.1 Generating Functional for Connected Green's Functions
625(2)
8.2.2 The Effective Action
627(4)
8.2.3 Effective Potential
631(1)
8.2.4 Loop Expansion
632(1)
8.3 Schwinger-Dyson Equations
633(9)
8.3.1 Derivation of Schwinger-Dyson Equations
633(3)
8.3.2 Ward and Ward-Takahashi Identities
636(6)
8.4 Renormalization
642(6)
8.4.1 Superficial Degree of Divergence
642(3)
8.4.2 Superficial Divergences in QED
645(3)
8.5 Renormalized QED
648(13)
8.5.1 QED Schwinger-Dyson Equations with Bare Fields
650(5)
8.5.2 Renormalized QED Green's Functions
655(4)
8.5.3 Renormalization Group
659(2)
8.6 Regularization
661(5)
8.6.1 Regularization Methods
661(3)
8.6.2 Dimensional Regularization
664(2)
8.7 Renormalized Perturbation Theory
666(20)
8.7.1 Renormalized Perturbation Theory for Φ4
666(5)
8.7.2 Renormalized Perturbative Yukawa Theory
671(1)
8.7.3 Renormalized Perturbative QED
672(9)
8.7.4 Minimal Subtraction Renormalization Schemes
681(2)
8.7.5 Running Coupling and Running Mass in QED
683(2)
8.7.6 Renormalization Group Flow and Fixed Points
685(1)
8.8 Spontaneous Symmetry Breaking
686(4)
8.9 Casimir Effect
690(3)
Summary
691(1)
Problems
692(1)
9 Nonabelian Gauge Theories
693(35)
9.1 Nonabelian Gauge Theories
693(5)
9.1.1 Formulation of Nonabelian Gauge Theories
693(3)
9.1.2 Wilson Lines and Wilson Loops
696(1)
9.1.3 Quantization of Nonabelian Gauge Theories
697(1)
9.2 Quantum Chromodynamics
698(17)
9.2.1 QCD Functional Integral
698(3)
9.2.2 Renormalization in QCD
701(2)
9.2.3 Running Coupling and Running Quark Mass
703(3)
9.2.4 BRST Invariance
706(2)
9.2.5 Lattice QCD
708(7)
9.3 Anomalies
715(4)
9.4 Introduction to the Standard Model
719(9)
9.4.1 Electroweak Symmetry Breaking
719(3)
9.4.2 Quarks and Leptons
722(3)
Summary
725(1)
Problems
726(2)
Appendix
728(26)
A.1 Physical Constants
728(1)
A.2 Notation and Useful Results
728(6)
A.2.1 Levi-Civita Tensor
729(1)
A.2.2 Dirac Delta Function and Jacobians
729(1)
A.2.3 Fourier Transforms
730(1)
A.2.4 Cauchy's Integral Theorem
730(1)
A.2.5 Wirtinger Calculus
731(1)
A.2.6 Exactness, Conservative Vector Fields and Integrating Factors
731(1)
A.2.7 Tensor and Exterior Products
732(2)
A.3 Dirac Algebra
734(2)
A.4 Euclidean Space Conventions
736(2)
A.5 Feynman Parameterization
738(1)
A.6 Dimensional Regularization
739(4)
A.7 Group Theory and Lie Groups
743(9)
A.7.1 Elements of Group Theory
743(2)
A.7.2 Lie Groups
745(3)
A.7.3 Unitary Representations of Lie Groups
748(4)
A.8 Results for Matrices
752(2)
References 754(10)
Index 764
Anthony G. Williams is Professor in Physics at Adelaide University, Australia. He has worked extensively in the areas of hadronic physics and computational physics, studying quark and gluon substructure. For this work, he was awarded the Walter Boas Medal by the Australian Institute of Physics in 2001 and elected Fellow of the American Physical Society in 2002. In 2020, he became the Deputy Director of the Centre for Dark Matter Particle Physics of the Australian Research Council.