Relativistic Quantum Mechanics

COURSE OUTLINE: You will learn Dirac and Klein-Gordon equations, Lorentz and Poincare groups, Fundamental processes of Quantum Electrodynamics. This course is taught by Professor Apoorva D Patel from IISc Bangalore

Mod-01 Lec-01 Introduction, The Klein-Gordon equation.
Mod-01 Lec-02 Particles and antiparticles, Two component framework.
Mod-01 Lec-03 Coupling to electromagnetism, Solution of the Coulomb problem.
Mod-01 Lec-04 Bohr-Sommerfeld semiclassical solution of the Coulomb problem.
Mod-01 Lec-05 Dirac matrices, Covariant form of the Dirac equation.
Mod-01 Lec-06 Electromagnetic interactions, Gyromagnetic ratio.
Mod-01 Lec-07 The Hydrogen atom problem, Symmetries, Parity, Separation of variables.
Mod-01 Lec-08 The Frobenius method solution, Energy levels and wavefunctions.
Mod-01 Lec-09 Non-relativistic reduction, The Foldy-Wouthuysen transformation.
Mod-01 Lec-10 Interpretation of relativistic corrections, Reflection from a potential barrier.
Mod-01 Lec-11 The Klein paradox, Pair creation process and examples.
Mod-01 Lec-12 Zitterbewegung, Hole theory and antiparticles.
Mod-01 Lec-13 Charge conjugation symmetry, Chirality, Projection operators.
Mod-01 Lec-14 Weyl and Majorana representations of the Dirac equation.
Mod-01 Lec-15 Time reversal symmetry, The PCT invariance.
Mod-01 Lec-16 Arrow of time and particle-antiparticle asymmetry, Band theory for graphene.
Mod-01 Lec-17 Dirac equation structure of low energy graphene states,.
Mod-02 Lec-18 Groups and symmetries, The Lorentz and Poincare groups.
Mod-02 Lec-19 Group representations, generators and algebra, Translations, rotations and boosts.
Mod-02 Lec-20 The spinor representation of SL(2,C), The spin-statistics theorem.
Mod-02 Lec-21 Finite dimensional representations of the Lorentz group, Euclidean and Galilean groups.
Mod-02 Lec-22 Classification of one particle states, The little group, Mass, spin and helicity.
Mod-02 Lec-23 Massive and massless one particle states.
Mod-02 Lec-24 P and T transformations, Lorentz covariance of spinors.
Mod-02 Lec-25 Lorentz group classification of Dirac operators, Orthogonality.
Mod-03 Lec-26 Propagator theory, Non-relativistic case and causality.
Mod-03 Lec-27 Relativistic case, Particle and antiparticle contributions, Feynman prescription.
Mod-03 Lec-28 Interactions and formal perturbative theory, The S-matrix and Feynman diagrams.
Mod-03 Lec-29 Trace theorems for products of Dirac matrices.
Mod-03 Lec-30 Photons and the gauge symmetry.
Mod-03 Lec-31 Abelian local gauge symmetry, The covariant derivative and invariants.
Mod-03 Lec-32 Charge quantisation, Photon propagator, Current conservation and polarisations.
Mod-03 Lec-33 Feynman rules for Quantum Electrodynamics, Nature of perturbative expansion.
Mod-03 Lec-34 Dyson\'s analysis of the perturbation series, Singularities of the S-matrix.
Mod-03 Lec-35 The T-matrix, Coulomb scattering.
Mod-03 Lec-36 Mott cross-section, Compton scattering.
Mod-03 Lec-37 Klein-Nishina result for cross-section.
Mod-03 Lec-38 Photon polarisation sums, Pair production through annihilation.
Mod-03 Lec-39 Unpolarised and polarised cross-sections.
Mod-03 Lec-40 Helicity properties, Bound state formation.
Mod-03 Lec-41 Bound state decay, Non-relativistic potentials.
Mod-03 Lec-42 Lagrangian formulation of QED, Divergences in Green\'s functions.
Mod-03 Lec-43 Infrared divergences due to massless particles, Renormalisation.
Mod-03 Lec-44 Symmetry constraints on Green\'s functions, Furry\'s theorem, Ward-Takahashi identity.
Mod-03 Lec-45 Status of QED, Organisation of perturbative expansion, Precision tests.