A Stroll through Quantum Fields (antecedent of Quantum Field Theory - From Basics to Modern Topics)

Contents
List of Figures and Tables
Preface
Acknowledgments
1 Basics of Quantum Field Theory
	1.1 Why Quantum Field Theory?
	1.2 Special Relativity
	1.3 Free Scalar Fields, Mode Decomposition
	1.4 Interacting Scalar Particles
	1.5 From Field Correlations to Reaction Rates
	1.6 Källen–Lehmann Spectral Representation
	1.7 Generating Functional
	Exercises
2 Perturbation Theory
	2.1 Perturbative Expansion and Feynman Rules
	2.2 Calculation of Loop Integrals
	2.3 Ultraviolet Divergences and Renormalization
	2.4 Perturbative Unitarity
	Exercises
3 Quantum Electrodynamics
	3.1 Spin-1/2 Fields
	3.2 Spin-1 Fields
	3.3 Quantum Electrodynamics
	3.4 Charge Conservation, Ward–Takahashi Identities
	3.5 Ultraviolet Renormalization
	3.6 Cutting Rules in QED and Unitarity
	3.7 Infrared Divergences
	Exercises
4 Spontaneous Symmetry Breaking
	4.1 Potential Energy Landscape
	4.2 Conserved Currents and Charges
	4.3 Spectral Properties
	4.4 Coleman’s Theorem
	4.5 Linear Sigma Model
	4.6 Heisenberg Model of Ferromagnetism
	Exercises
5 Functional Quantization
	5.1 Path Integral in Quantum Mechanics
	5.2 Functional Manipulations
	5.3 Path Integral in Scalar Field Theory
	5.4 Functional Determinants
	5.5 Quantum Effective Action
	5.6 Two-Particle Irreducible Effective Action
	5.7 Euclidean Path Integral and Statistical Mechanics
	Exercises
6 Path Integrals for Fermions and Photons
	6.1 Grassmann Variables
	6.2 Path Integral for Fermions
	6.3 Path Integral for Photons
	6.4 Schwinger–Dyson Equations
	6.5 Quantum Anomalies
	Exercises
7 Non-Abelian Gauge Symmetry
	7.1 Non-Abelian Lie Groups and Algebras
	7.2 Yang–Mills Lagrangian
	7.3 Non-Abelian Gauge Theories
	7.4 Spontaneous Gauge Symmetry Breaking
	7.5 θ-term and Strong-CP Problem
	7.6 Non-Local Gauge Invariant Operators
	Exercises
8 Quantization of Yang–Mills Theory
	8.1 Naive Quantization of the Gauge Bosons
	8.2 Gauge Fixing
	8.3 Fadeev–Popov Quantization and Ghost Fields
	8.4 Feynman Rules for Non-Abelian Gauge Theories
	8.5 On-Shell Non-Abelian Ward–Takahashi Identities
	8.6 Ghosts and Unitarity
	Exercises
9 Renormalization of Gauge Theories
	9.1 Ultraviolet Power Counting
	9.2 Symmetries of the Quantum Effective Action
	9.3 Renormalizability
	9.4 Background Field Method
	Exercises
10 Renormalization Group
	10.1 Scale Dependence of Correlation Functions
	10.2 Correlators Containing Composite Operators
	10.3 Operator Product Expansion
	10.4 Example: QCD Corrections to Weak Decays
	10.5 Non-Perturbative Renormalization Group
	Exercises
11 Effective Field Theories
	11.1 General Principles of Effective Theories
	11.2 Example: Fermi Theory of Weak Decays
	11.3 The Standard Model as an Effective Field Theory
	11.4 Effective Theories in QCD
	11.5 EFT of Spontaneous Symmetry-Breaking
	Exercises
12 Quantum Anomalies
	12.1 Axial Anomalies in a Gauge Background
	12.2 Generalizations
	12.3 Wess–Zumino Consistency Conditions
	12.4 ’t Hooft Anomaly Matching
	12.5 Scale Anomalies
	Exercises
13 Localized Field Configurations
	13.1 Domain Walls
	13.2 Monopoles
	13.3 Instantons
	13.4 Skyrmions
	Exercises
14 Modern Tools for Tree Amplitudes
	14.1 Color Decomposition of Gluon Amplitudes
	14.2 Spinor-Helicity Formalism
	14.3 Britto–Cachazo–Feng–Witten On-Shell Recursion
	14.4 Tree-Level Gravitational Amplitudes
	14.5 Cachazo–Svrcek–Witten Rules
	Exercises
15 Worldline Formalism
	15.1 Worldline Representation
	15.2 Quantum Electrodynamics
	15.3 Schwinger Mechanism
	15.4 Calculation of One-Loop Amplitudes
	Exercises
16 Lattice Field Theory
	16.1 Discretization of Bosonic Actions
	16.2 Lattice Fermions
	16.3 Hadron Mass Determination on the Lattice
	16.4 Wilson Loops and Color Confinement
	16.5 Gauge Fixing on the Lattice
	16.6 Lattice Hamiltonian
	16.7 Lattice Worldline Formalism
	Exercises
17 Quantum Field Theory at Finite Temperature
	17.1 Canonical Thermal Ensemble
	17.2 Finite-T Perturbation Theory
	17.3 Large-Distance Effective Theories
	17.4 Out-of-Equilibrium Systems
	Exercises
18 Strong Fields and Semi-Classical Methods
	18.1 Situations Involving Strong Fields
	18.2 Observables at Leading and Next-to-Leading Orders
	18.3 Green’s Formulas
	18.4 Mode Functions
	18.5 Multi-Point Correlation Functions at Tree Level
	Exercises
19 From Trees to Loops
	19.1 Dualities Between Loops and Trees
	19.2 Reduction of One-Loop Amplitudes
	19.3 One-Loop Amplitudes from Unitarity Cuts
	19.4 The Frontier: Multi-Loop Amplitudes
	Exercises
Further Reading
Index