File : pdf, 2.8 MB, 349 pages
by Peter S. Riseborough
TOC
1 Introduction
2 Quantum Mechanics of a Single Photon
2.1 Rotations and Intrinsic Spin
2.2 Massless Particles with Spin Zero
2.3 Massless Particles with Spin One
3 Maxwell’s Equations
3.1 Vector and Scalar Potentials
3.2 Gauge Invariance .
4 Relativistic Formulation of Electrodynamics
4.1 Lorentz Scalars and Vectors
4.2 Covariant and Contravariant Derivatives
4.3 Lorentz Transformations
4.4 Invariant Form of Maxwell’s Equations
5 The Simplest Classical Field Theory
5.1 The Continuum Limit
5.2 Normal Modes
5.3 Rules of Canonical Quantization
5.4 The Algebra of Boson Operators
5.5 The Classical Limit
6 Classical Field Theory
6.1 The Hamiltonian Formulation
6.2 Symmetry and Conservation Laws
6.3 The Energy-Momentum Tensor
7 The Electromagnetic Lagrangian
7.1 Conservation Laws for Electromagnetic Fields
7.2 Massive Spin-One Particles
8 Symmetry Breaking and Mass Generation
8.1 Symmetry Breaking and Goldstone Bosons
8.2 The Kibble-Higgs Mechanism
9 Quantization of the Electromagnetic Field
9.1 The Lagrangian and Hamiltonian Density
9.2 Quantizing the Normal Modes
9.2.1 The Energy of the Field
9.2.2 The Electromagnetic Field
9.2.3 The Momentum of the Field
9.2.4 The Angular Momentum of the Field
9.3 Uncertainty Relations
9.4 Coherent States
9.4.1 The Phase-Number Uncertainty Relation
9.4.2 Argand Representation of Coherent States
10 Non-Relativistic Quantum Electrodynamics
10.1 Emission and Absorption of Photons
10.1.1 The Emission of Radiation
10.1.2 The Dipole Approximation
10.1.3 Electric Dipole Radiation Selection Rules
10.1.4 Angular Distribution of Dipole Radiation
10.1.5 The Decay Rate from Dipole Transitions
10.1.6 The 2p ! 1s Electric Dipole Transition Rate
10.1.7 Electric Quadrupole and Magnetic Dipole Transitions
10.1.8 The 3d ! 1s Electric Quadrupole Transition Rate
10.1.9 Two-photon decay of the 2s state of Hydrogen
10.1.10 The Absorption of Radiation
10.1.11 The Photoelectric Effect
10.1.12 Impossibility of absorption of photons by free-electrons
10.2 Scattering of Light
10.3 Renormalization
11 The Dirac Equation
11.1 Conservation of Probability
11.2 Covariant Form of the Dirac Equation
11.3 The Field Free Solution
11.4 Coupling to Fields
11.5 Lorentz Covariance of the Dirac Equation
11.6 The Non-Relativistic Limit
11.7 Conservation of Angular Momentum
11.8 Conservation of Parity
11.9 Bi-linear Covariants
11.10 The Spherically Symmetric Dirac Equation
11.11 Scattering by a Spherically Symmetric Potential
11.12 An Electron in a Uniform Magnetic Field
11.13 Motion of an Electron in a Classical Electromagnetic Field
11.14 The Limit of Zero Mass
11.15 Classical Dirac Field Theory
11.16 Hole Theory
12 The Many-Particle Dirac Field
12.1 Second Quantization of Fermions
12.2 Quantizing the Dirac Field
12.3 The CPT Theorem
12.4 The Connection between Spin and Statics
13 Massive Gauge Field Theory
13.1 The Gauge Symmetry
13.2 The Coupling to the Gauge Field
13.3 The Free Gauge Fields
13.4 Breaking the Symmetry
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