Quantum Field Theory A Modern Introduction

Quantum Field Theory A Modern Introduction
	Half-Title
	Title Page
	Copyright
	Dedication
	Preface
	Acknowledgments
	Contents
Part I: Quantum Fields and Renormalization
	1. Why Quantum Field Theory?
		1.1 Historical Perspective
		1.2 Strong Interactions
		1.3 Weak Interactions
		1.4 Gravitational Interaction
		1.5 Gauge Revolution
		1.6 Unification
		1.7 Action Principle
		1.8 From First to Second Quantization
		1.9 Noether's Theorem
		1.10 Exercises
	2. Symmetries and Group Theory
		2.1 Elements of Group Theory
		2.2 SO(2)
		2.3 Representations of SO(2) and U(1)
		2.4 Representations of SO(3) and SU(2)
		2.5 Representations of SO(N)
		2.6 Spinors
		2.7 Lorentz Group
		2.8 Representations of the Poincaré Group
		2.9 Master Groups and Supersymmetry
		2.10 Exercises
	3. Spin-0 and ½ Fields
		3.1 Quantization Schemes
		3.2 Klein-Gordon Scalar Field
		3.3 Charged Scalar Field
		3.4 Propagator Theory
		3.5 Dirac Spinor Field
		3.6 Quantizing the Spinor Field
		3.7 Weyl Neutrinos
		3.8 Exercises
	4. Quantum Electrodynamics
		4.1 Maxwell's Equations
		4.2 Relativistic Quantum Mechanics
		4.3 Quantizing the Maxwell Field
		4.4 Gupta-Bleuler Quantization
		4.5 C, P, and T Invariance
			4.5.1 Parity
			4.5.2 Charge Conjugation
			4.5.3 Time Reversal
		4.6 CPT Theorem
		4.7 Exercises
	5. Feynman Rules and LSZ Reduction
		5.1 Cross Sections
		5.2 Propagator Theory and Rutherford Scattering
		5.3 LSZ Reduction Formulas
		5.4 Reduction of Dirac Spinors
		5.5 Time Evolution Operator
		5.6 Wick's Theorem
		5.7 Feynman's Rules
		5.8 Exercises
	6. Scattering Processes and the S Matrix
		6.1 Compton Effect
		6.2 Pair Annihilation
		6.3 Møller Scattering
		6.4 Bhabha Scattering
		6.5 Bremsstrahlung
		6.6 Radiative Corrections
		6.7 Anomalous Magnetic Moment
		6.8 Infrared Divergence
		6.9 Lamb Shift
		6.10 Dispersion Relations
		6.11 Exercises
	7. Renormalization of QED
		7.1 The Renormalization Program
		7.2 Renormalization Types
			7.2.1 Nonrenormalizable Theories
			7.2.2 Renormalizable Theories
			7.2.3 Super-renormalizable Theories
			7.2.4 Finite Theories
		7.3 Overview of Renormalization in ϕ⁴ Theory
		7.4 Overview of Renormalization in QED
		7.5 Types of Regularization
		7.6 Ward-Takahashi Identities
		7.7 Overlapping Divergences
		7.8 Renormalization of QED
			7.8.1 Step One
			7.8.2 Step Two
			7.8.3 Step Three
			7.8.4 Step Four
		7.9 Exercises
Part II: Gauge Theory and the Standard Model
	8. Path Integrals
		8.1 Postulates of Quantum Mechanics
			8.1.1 Postulate I
			8.1.2 Postulate II
		8.2 Derivation of the Schrödinger Equation
		8.3 From First to Second Quantization
		8.4 Generator of Connected Graphs
		8.5 Loop Expansion
		8.6 Integration over Grassmann Variables
		8.7 Schwinger-Dyson Equations
		8.8 Exercises
	9. Gauge Theory
		9.1 Local Symmetry
		9.2 Faddeev-Popov Gauge Fixing
		9.3 Feynman Rules for Gauge Theory
		9.4 Coulomb Gauge
		9.5 The Gribov Ambiguity
		9.6 Equivalence of the Coulomb and Landau Gauge
		9.7 Exercises
	10. The Weinberg-Salam Model
		10.1 Broken Symmetry in Nature
		10.2 The Higgs Mechanism
		10.3 Weak Interactions
		10.4 Weinberg-Salam Model
		10.5 Lepton Decay
		10.6 R_ξ Gauge
		10.7 't Hooft Gauge
		10.8 Coleman-Weinberg Mechanism
		10.9 Exercises
	11. The Standard Model
		11.1 The Quark Model
		11.2 QCD
			11.2.1 Spin-Statistics Problem
			11.2.2 Pair Annihilation
			11.2.3 Jets
			11.2.4 Absence of Exotics
			11.2.5 Pion Decay
			11.2.6 Asymptotic Freedom
			11.2.7 Confinement
			11.2.8 Chiral Symmetry
			11.2.9 No Anomalies
		11.3 Jets
		11.4 Current Algebra
		11.5 PCAC and the Adler-Weisberger Relation
			11.5.1 CVC
			11.5.2 PCAC
			11.5.3 Adler-Weisberger Relation
		11.6 Mixing Angle and Decay Processes
			11.6.1 Purely Leptonic Decays
			11.6.2 Semileptonic Decays
			11.6.3 Nonleptonic Decays
		11.7 GIM Mechanism and Kobayashi-Maskawa Matrix
		11.8 Exercises
	12. Ward Identities, BRST, and Anomalies
		12.1 Ward-Takahashi Identity
		12.2 Slavnov-Taylor Identities
		12.3 BRST Quantization
		12.4 Anomalies
		12.5 Non-Abelian Anomalies
		12.6 QCD and Pion Decay into Gamma Rays
		12.7 Fujikawa's Method
		12.8 Exercises
	13. BPHZ Renormalization of Gauge Theories
		13.1 Counterterms in Gauge Theory
		13.2 Dimensional Regularization of Gauge Theory
		13.3 BPHZ Renormalization
		13.4 Forests and Skeletons
		13.5 Does Quantum Field Theory Really Exist?
		13.6 Exercises
	14. QCD and the Renormalization Group
		14.1 Deep Inelastic Scattering
		14.2 Parton Model
		14.3 Neutrino Sum Rules
		14.4 Product Expansion at the Light-Cone
		14.5 Renormalization Group
		14.6 Asymptotic Freedom
		14.7 Callan-Symanzik Relation
		14.8 Minimal Subtraction
		14.9 Scale Violations
		14.10 Renormalization Group Proof
			14.10.1 Step One
			14.10.2 Step Two
			14.10.3 Step Three
		14.11 Exercises
Part III: Nonperturbative Methods and Unification
	15. Lattice Gauge Theory
		15.1 The Wilson Lattice
		15.2 Scalars and Fermions on the Lattice
		15.3 Confinement
		15.4 Strong Coupling Approximation
		15.5 Monte Carlo Simulations
		15.6 Hamiltonian Formulation
		15.7 Renormalization Group
		15.8 Exercises
	16. Solitons, Monopoles, and Instantons
		16.1 Solitons
			16.1.1 Example: ϕ⁴
			16.1.2 Example: Sine-Gordon Equation
			16.1.3 Example: Nonlinear O(3) Model
		16.2 Monopole Solutions
		16.3 't Hooft-Polyakov Monopole
		16.4 WKB, Tunneling, and Instantons
		16.5 Yang-Mills Instantons
		16.6 θ Vacua and the Strong CP Problem
		16.7 Exercises
	17. Phase Transitions and Critical Phenomena
		17.1 Critical Exponents
		17.2 The Ising Model
			17.2.1 XYZ Heisenberg Model
			17.2.2 IRF and Vertex Models
		17.3 Yang-Baxter Relation
		17.4 Mean-Field Approximation
		17.5 Scaling and the Renormalization Group
			17.5.1 Step One
			17.5.2 Step Two
			17.5.3 Step Three
			17.5.4 Step Four
		17.6 ϵ Expansion
		17.7 Exercises
	18. Grand Unified Theories
		18.1 Unification and Running Coupling Constants
		18.2 SU(5)
		18.3 Anomaly Cancellation
		18.4 Fermion Representation
		18.5 Spontaneous Breaking of SU(5)
		18.6 Hierarchy Problem
		18.7 SO(10)
		18.8 Beyond GUT
			18.8.1 Technicolor
			18.8.2 Preons or Subquarks
			18.8.3 Supersymmetry and Superstrings
		18.9 Exercises
	19. Quantum Gravity
		19.1 Equivalence Principle
		19.2 Generally Covariant Action
		19.3 Vierbeins and Spinors in General Relativity
		19.4 GUTs and Cosmology
		19.5 Inflation
		19.6 Cosmological Constant Problem
		19.7 Kaluza-Klein Theory
		19.8 Generalization to Yang-Mills Theory
		19.9 Quantizing Gravity
		19.10 Counterterms in Quantum Gravity
		19.11 Exercises
	20. Supersymmetry and Supergravity
		20.1 Supersymmetry
		20.2 Supersymmetric Actions
		20.3 Superspace
		20.4 Supersymmetric Feynman Rules
		20.5 Nonrenormalization Theorems
		20.6 Finite Field Theories
		20.7 Super Groups
		20.8 Supergravity
		20.9 Exercises
	21. Superstrings
		21.1 Why Strings?
		21.2 Points versus Strings
		21.3 Quantizing the String
			21.3.1 Gupta-Bleuler Quantization
			21.3.2 Light-Cone Gauge
			21.3.3 BRST Quantization
		21.4 Scattering Amplitudes
		21.5 Superstrings
		21.6 Types of Strings
			21.6.1 Type I
			21.6.2 Type IIA
			21.6.3 Type lIB
			21.6.4 Heterotic String
		21.7 Higher Loops
		21.8 Phenomenology
		21.9 Light-Cone String Field Theory
		21.10 BRST Action
		21.11 Exercises
Appendix
	A.1 SU(N)
	A.2 Tensor Products
	A.3 SU(3)
	A.4 Lorentz Group
	A.S Dirac Matrices
	A.6 Infrared Divergences to All Orders
	A.7 Dimensional Regularization
Notes
	Chapter 1. Why Quantum Field Theory?
	Chapter 3. Spin 0 and ½ Fields
	Chapter 4. Quantum Electrodynamics
	Chapter 5. Feynman Rules and Reduction
	Chapter 6. Scattering Processes and the S-Matrix
	Chapter 7. Renormalization of QED
	Chapter 8. Path Integrals
	Chapter 9. Gauge Theory
	Chapter 10. The Weinberg-Salam Model
	Chapter 11. The Standard Model
	Chapter 12. Ward Identities, BRST, and Anomalies
	Chapter 13. BPHZ Renormalization of Gauge Theories
	Chapter 14. QCD and the Renormalization Group
	Chapter 15. Lattice Gauge Theory
	Chapter 16. Solitons, Monopoles, and Instantons
	Chapter 17. Phase Transitions and Critical Phenomena
	Chapter 18. Grand Unified Theories
	Chapter 19. Quantum Gravity
	Chapter 20. Supersymmetry and Supergravity
	Chapter 21. Superstrings
References
	Field Theory
	Gauge Theories
	Particle Physics
	Critical and Non-Perturbative Phenomena
	Supergravity
	Superstrings
Index
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