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