Learn · Relativistic Quantum Mechanics
Lecture 31 of 45Quantum Electrodynamics
Abelian local gauge symmetry, The covariant derivative and invariants
Prof. Apoorva D Patel · IISc Bangalore
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All the lectures
- Introduction, The Klein-Gordon equation
- Particles and antiparticles, Two component framework
- Coupling to electromagnetism, Solution of the Coulomb problem
- Bohr-Sommerfeld semiclassical solution of the Coulomb problem, The Dirac equation and the Clifford algebra
- Dirac matrices, Covariant form of the Dirac equation, Equations of motion, Spin, Free particle solutions
- Electromagnetic interactions, Gyromagnetic ratio
- The Hydrogen atom problem, Symmetries, Parity, Separation of variables
- The Frobenius method solution, Energy levels and wavefunctions
- Non-relativistic reduction, The Foldy-Wouthuysen transformation
- Interpretation of relativistic corrections, Reflection from a potential barrier
- The Klein paradox, Pair creation process and examples
- Zitterbewegung, Hole theory and antiparticles
- Charge conjugation symmetry, Chirality, Projection operators, The Weyl equation
- Weyl and Majorana representations of the Dirac equation, Unitary and antiunitary symmetries
- Time reversal symmetry, The PCT invariance
- Arrow of time and particle-antiparticle asymmetry, Band theory for graphene
- Dirac equation structure of low energy graphene states, Relativistic signatures in graphene properties
- Groups and symmetries, The Lorentz and Poincare groups
- Group representations, generators and algebra, Translations, rotations and boosts
- The spinor representation of SL(2,C), The spin-statistics theorem
- Finite dimensional representations of the Lorentz group, Euclidean and Galilean groups
- Classification of one particle states, The little group, Mass, spin and helicity
- Massive and massless one particle states
- P and T transformations, Lorentz covariance of spinors
- Lorentz group classification of Dirac operators, Orthogonality and completeness of Dirac spinors, Projection operators
- Propagator theory, Non-relativistic case and causality
- Relativistic case, Particle and antiparticle contributions, Feynman prescription and the propagator
- Interactions and formal perturbative theory, The S-matrix and Feynman diagrams
- Trace theorems for products of Dirac matrices
- Photons and the gauge symmetry
- Abelian local gauge symmetry, The covariant derivative and invariants
- Charge quantisation, Photon propagator, Current conservation and polarisations
- Feynman rules for Quantum Electrodynamics, Nature of perturbative expansion
- Dyson's analysis of the perturbation series, Singularities of the S-matrix, Elementary QED processes
- The T-matrix, Coulomb scattering
- Mott cross-section, Compton scattering
- Klein-Nishina result for cross-section
- Photon polarisation sums, Pair production through annihilation
- Unpolarised and polarised cross-sections
- Helicity properties, Bound state formation
- Bound state decay, Non-relativistic potentials
- Lagrangian formulation of QED, Divergences in Green's functions, Superficially divergent 1-loop diagrams and regularisation
- Infrared divergences due to massless particles, Renormalisation and finite physical results
- Symmetry constraints on Green's functions, Furry's theorem, Ward-Takahashi identity, Spontaneous breaking of gauge symmetry and superconductivity
- Status of QED, Organisation of perturbative expansion, Precision tests