A First Book Of Quantum Field Theory

A First Book Of Quantum Field Theory Second Edition
	Half-Title
	Title-Page
	Copyright
	Preface to the second edition
	Preface to the first edition
	Notations
	Contents
Chapter 1 Preliminaries
	1.1 Why Quantum Field Theory
	1.2 Creation and annihilation operators
	1.3 Special relativity
	1.4 Space and time in relativistic quantum theory
	1.5 Natural units
Chapter 2 Classical Field Theory
	2.1 A quick review of particle mechanics
		2.1.1 Action principle and Euler-Lagrange equations
		2.1.2 Hamiltonian formalism and Poisson brackets
	2.2 Euler-Lagrange equations in field theory
		2.2.1 Action functional and Lagrangian
		2.2.2 Euler-Lagrange equations
	2.3 Hamiltonian formalism
	2.4 Noether's theorem
Chapter 3 Quantization of scalar fields
	3.1 Equation of motion
	3.2 The field and its canonical quantization
	3.3 Fourier decomposition of the field
	3.4 Ground state of the Hamiltonian and normal ordering
	3.5 Fock space
	3.6 Complex scalar field
		3.6.1 Creation and annihilation operators
		3.6.2 Particles and antiparticles
		3.6.3 Ground state and Hamiltonian
	3.7 Propagator
Chapter 4 Quantization of Dirac fields
	4.1 Dirac Hamiltonian
	4.2 Dirac equation
	4.3 Plane wave solutions of Dirac equation
		4.3.1 Positive and negative energy spinors
		4.3.2 Explicit solutions in Dirac-Pauli representation
	4.4 Projection operators
		4.4.1 Projection operators for positive and negative energy states
		4.4.2 Helicity projection operators
		4.4.3 Chirality projection operators
		4.4.4 Spin projection operators
	4.5 Lagrangian for a Dirac field
	4.6 Fourier decomposition of the field
	4.7 Propagator
Chapter 5 The S-matrix expansion
	5.1 Examples of interactions
	5.2 Evolution operator
	5.3 S-matrix
	5.4 Wick's theorem
Chapter 6 From Wick expansion to
Feynman diagrams
	6.1 Yukawa interaction : decay of a scalar
	6.2 Normalized states
	6.3 Sample calculation of a matrix element
	6.4 Another example: fermion scattering
	6.5 Feynman amplitude
	6.6 Feynman rules
	6.7 Virtual particles
	6.8 Amplitudes which are not S-matrix elements
Chapter 7 Cross sections and decay rates
	7.1 Decay rate
	7.2 Examples of decay rate calculation
		7.2.1 Decay of a scalar into a fermion-antifermion pair
		7.2.2 Muon decay with 4-fermion interaction
	7.3 Scattering cross section
	7.4 Generalities of 2-to-2 scattering
		7.4.1 CM frame
		7.4.2 Lab frame
	7.5 Inelastic scattering with 4-fermion interaction
		7.5.1 Cross-section in CM frame
		7.5.2 Cross-section in Lab frame
	7.6 Mandelstam variables
Chapter 8 Quantization of the electromagnetic field
	8.1 Classical theory of electromagnetic fields
	8.2 Problems with quantization
	8.3 Modifying the classical Lagrangian
	8.4 Propagator
	8.5 Fourier decomposition of the field
	8.6 Physical states
	8.7 Another look at the propagator
	8.8 Feynman rules for photons
Chapter 9 Quantum electrodynamics
	9.1 Local gauge invariance
	9.2 Interaction Hamiltonian
	9.3 Lowest order processes
	9.4 Electron-electron scattering
	9.5 Electron-positron scattering
	9.6 Electron-Positron to Muon-Antimuon
	9.7 Consequence of gauge invariance
	9.8 Compton scattering
	9.9 Scattering by an external field
	9.10 Bremsstrahlung
Chapter 10 P, T, C and their combinations
	10.1 Motivations from classical physics
	10.2 Parity
		10.2.1 Free scalar fields
		10.2.2 Free Dirac field
		10.2.3 Free photon field
		10.2.4 Interacting fields
	10.3 Charge conjugation
		10.3.1 Free fields
		10.3.2 Interactions
	10.4 Time reversal
		10.4.1 Antilinearity
		10.4.2 Free fields
		10.4.3 Interactions
	10.5 CP
	10.6 CPT
Chapter 11 Electromagnetic form factors
	11.1 General electromagnetic vertex
	11.2 Physical interpretation of form factors
		11.2.1 Charge form factor F1
		11.2.2 Anomalous magnetic moment F2
		11.2.4 Anapole moment F3
	11.3 Anomalous magnetic moment of the electron
	11.4 Charge form factor
	11.5 Electron-proton scattering
Chapter 12 Renormalization
	12.1 Degree of divergence of a diagram
		12.1.1 Superficial degree of divergence
		12.1.2 Superficial vs. real degree of divergence
	12.2 Specific examples in QED
	12.3 Outline of the program
	12.4 Ward-Takahashi identity
	12.5 General forms for divergent amplitudes
		12.5.1 Fermion self-energy
		12.5.2 Vacuum polarization
		12.5.3 Vertex function
	12.6 Regularization of self-energy diagrams
		12.6.1 Vacuum polarization diagram
		12.6.2 Fermion self-energy diagram
	12.7 Counterterms
		12.7.1 Vacuum polarization diagram
		12.7.2 Fermion self-energy diagram
		12.7.3 Vertex function
	12.8 Full Lagrangian
	12.9 Observable effects of renormalization
		12.9.1 Modification of Coulomb interaction
		12.9.2 Running coupling constant
		12.9.3 Cancellation of infra-red divergences
Chapter 13 Symmetries and symmetry
breaking
	13.1 Classification of symmetries
	13.2 Groups and symmetries
		13.2.1 Symmetry group
		13.2.2 Examples of continuous symmetry groups
		13.2.3 Generators of continuous groups
		13.2.4 Representations
	13.3 Approximate symmetries
	13.4 Spontaneous breaking of symmetries
		13.4.1 Discrete symmetry
		13.4.2 U(1) symmetry
		13.4.3 Non-Abelian symmetry
	13.5 Goldstone's theorem
		13.5.1 Appearance of massless states
		13.5.2 Examples of Nambu-Goldstone bosons
		13.5.3 Interaction of Goldstone bosons
	13.6 Higgs mechanism
Chapter 14 Yang-Mills theory of
non-Abelian gauge fields
	14.1 Gauge fields of non-Abelian symmetry
	14.2 Pure gauge Lagrangian
	14.3 Interactions of non-Abelian gauge fields
		14.3.1 Gauge interactions of other particles
		14.3.2 Self-interactions of gauge bosons
	14.4 Equations of motion and conserved currents
	14.5 Quantization of non-Abelian gauge fields
	14.6 Quantum Chromodynamics
Chapter 15 Standard electroweak theory
	15.1 Gauge group
		15.1.1 Choice of gauge group
		15.1.2 Pure gauge Lagrangian
	15.2 Spontaneous symmetry breaking
		15.2.1 Introducing the Higgs boson multiplet
		15.2.2 Gauge boson masses
		15.2.3 Scalar modes
	15.3 Fermions in the theory
		15.3.1 Gauge interactions
		15.3.2 Electron mass
		15.3.3 Yukawa couplings
		15.3.4 Other fermions in the model
	15.4 Gauge boson decay
	15.5 Scattering processes
		15.5.1 Forward-backward asymmetry
		15.5.2 Low energy weak interactions
		15.5.3 High energy scattering
	15.6 Propagator for unstable particles
	15.7 Global symmetries of the model
Appendix A Useful formulas
Appendix B Answers to selected exercises
Index
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