Physics - Relativistic Quantum Mechanics (English)

2    Monday, May 12, 2025   

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Lecture 1: Mod-01 Lec-01 Introduction, The Klein-Gordon equation

Lecture 2: Mod-01 Lec-02 Particles and antiparticles, Two component framework

Lecture 3: Mod-01 Lec-03 Coupling to electromagnetism, Solution of the Coulomb problem

Lecture 4: Mod-01 Lec-04 Bohr-Sommerfeld semiclassical solution of the Coulomb problem

Lecture 5: Mod-01 Lec-05 Dirac matrices, Covariant form of the Dirac equation

Lecture 6: Mod-01 Lec-06 Electromagnetic interactions, Gyromagnetic ratio

Lecture 7: Mod-01 Lec-07 The Hydrogen atom problem, Symmetries, Parity, Separation of variables

Lecture 8: Mod-01 Lec-08 The Frobenius method solution, Energy levels and wavefunctions

Lecture 9: Mod-01 Lec-09 Non-relativistic reduction, The Foldy-Wouthuysen transformation

Lecture 10: Mod-01 Lec-10 Interpretation of relativistic corrections, Reflection from a potential barrier

Lecture 11: Mod-01 Lec-11 The Klein paradox, Pair creation process and examples

Lecture 12: Mod-01 Lec-12 Zitterbewegung, Hole theory and antiparticles

Lecture 13: Mod-01 Lec-13 Charge conjugation symmetry, Chirality, Projection operators

Lecture 14: Mod-01 Lec-14 Weyl and Majorana representations of the Dirac equation

Lecture 15: Mod-01 Lec-15 Time reversal symmetry, The PCT invariance

Lecture 16: Mod-01 Lec-16 Arrow of time and particle-antiparticle asymmetry, Band theory for graphene

Lecture 17: Mod-01 Lec-17 Dirac equation structure of low energy graphene states,

Lecture 18: Mod-02 Lec-18 Groups and symmetries, The Lorentz and Poincare groups

Lecture 19: Mod-02 Lec-19 Group representations, generators and algebra, Translations, rotations and boosts

Lecture 20: Mod-02 Lec-20 The spinor representation of SL(2,C), The spin-statistics theorem

Lecture 21: Mod-02 Lec-21 Finite dimensional representations of the Lorentz group, Euclidean and Galilean groups

Lecture 22: Mod-02 Lec-22 Classification of one particle states, The little group, Mass, spin and helicity

Lecture 23: Mod-02 Lec-23 Massive and massless one particle states

Lecture 24: Mod-02 Lec-24 P and T transformations, Lorentz covariance of spinors

Lecture 25: Mod-02 Lec-25 Lorentz group classification of Dirac operators, Orthogonality

Lecture 26: Mod-03 Lec-26 Propagator theory, Non-relativistic case and causality

Lecture 27: Mod-03 Lec-27 Relativistic case, Particle and antiparticle contributions, Feynman prescription

Lecture 28: Mod-03 Lec-28 Interactions and formal perturbative theory, The S-matrix and Feynman diagrams

Lecture 29: Mod-03 Lec-29 Trace theorems for products of Dirac matrices

Lecture 30: Mod-03 Lec-30 Photons and the gauge symmetry

Lecture 31: Mod-03 Lec-31 Abelian local gauge symmetry, The covariant derivative and invariants

Lecture 32: Mod-03 Lec-32 Charge quantisation, Photon propagator, Current conservation and polarisations

Lecture 33: Mod-03 Lec-33 Feynman rules for Quantum Electrodynamics, Nature of perturbative expansion

Lecture 34: Mod-03 Lec-34 Dyson\'s analysis of the perturbation series, Singularities of the S-matrix

Lecture 35: Mod-03 Lec-35 The T-matrix, Coulomb scattering

Lecture 36: Mod-03 Lec-36 Mott cross-section, Compton scattering

Lecture 37: Mod-03 Lec-37 Klein-Nishina result for cross-section

Lecture 38: Mod-03 Lec-38 Photon polarisation sums, Pair production through annihilation

Lecture 39: Mod-03 Lec-39 Unpolarised and polarised cross-sections

Lecture 40: Mod-03 Lec-40 Helicity properties, Bound state formation

Lecture 41: Mod-03 Lec-41 Bound state decay, Non-relativistic potentials

Lecture 42: Mod-03 Lec-42 Lagrangian formulation of QED, Divergences in Green\'s functions

Lecture 43: Mod-03 Lec-43 Infrared divergences due to massless particles, Renormalisation

Lecture 44: Mod-03 Lec-44 Symmetry constraints on Green\'s functions, Furry\'s theorem, Ward-Takahashi identity

Lecture 45: Mod-03 Lec-45 Status of QED, Organisation of perturbative expansion, Precision tests