Relativistic Quantum Mechanics

Lectures

Klein-Gordon and Dirac Equations

1. Introduction, The Klein-Gordon equation Video
2. Particles and antiparticles, Two component framework Video
3. Coupling to electromagnetism, Solution of the Coulomb problem Video
4. Bohr-Sommerfeld semiclassical solution of the Coulomb problem, The Dirac equation and the Clifford algebra Video
5. Dirac matrices, Covariant form of the Dirac equation, Equations of motion, Spin, Free particle solutions Video
6. Electromagnetic interactions, Gyromagnetic ratio Video
7. The Hydrogen atom problem, Symmetries, Parity, Separation of variables Video
8. The Frobenius method solution, Energy levels and wavefunctions Video
9. Non-relativistic reduction, The Foldy-Wouthuysen transformation Video
10. Interpretation of relativistic corrections, Reflection from a potential barrier Video
11. The Klein paradox, Pair creation process and examples Video
12. Zitterbewegung, Hole theory and antiparticles Video
13. Charge conjugation symmetry, Chirality, Projection operators, The Weyl equation Video
14. Weyl and Majorana representations of the Dirac equation, Unitary and antiunitary symmetries Video
15. Time reversal symmetry, The PCT invariance Video
16. Arrow of time and particle-antiparticle asymmetry, Band theory for graphene Video
17. Dirac equation structure of low energy graphene states, Relativistic signatures in graphene properties Video

Lorentz and Poincare Groups

18. Groups and symmetries, The Lorentz and Poincare groups Video
19. Group representations, generators and algebra, Translations, rotations and boosts Video
20. The spinor representation of SL(2,C), The spin-statistics theorem Video
21. Finite dimensional representations of the Lorentz group, Euclidean and Galilean groups Video
22. Classification of one particle states, The little group, Mass, spin and helicity Video
23. Massive and massless one particle states Video
24. P and T transformations, Lorentz covariance of spinors Video
25. Lorentz group classification of Dirac operators, Orthogonality and completeness of Dirac spinors, Projection operators Video

Quantum Electrodynamics

26. Propagator theory, Non-relativistic case and causality Video
27. Relativistic case, Particle and antiparticle contributions, Feynman prescription and the propagator Video
28. Interactions and formal perturbative theory, The S-matrix and Feynman diagrams Video
29. Trace theorems for products of Dirac matrices Video
30. Photons and the gauge symmetry Video
31. Abelian local gauge symmetry, The covariant derivative and invariants Video
32. Charge quantisation, Photon propagator, Current conservation and polarisations Video
33. Feynman rules for Quantum Electrodynamics, Nature of perturbative expansion Video
34. Dyson's analysis of the perturbation series, Singularities of the S-matrix, Elementary QED processes Video
35. The T-matrix, Coulomb scattering Video
36. Mott cross-section, Compton scattering Video
37. Klein-Nishina result for cross-section Video
38. Photon polarisation sums, Pair production through annihilation Video
39. Unpolarised and polarised cross-sections Video
40. Helicity properties, Bound state formation Video
41. Bound state decay, Non-relativistic potentials Video
42. Lagrangian formulation of QED, Divergences in Green's functions, Superficially divergent 1-loop diagrams and regularisation Video
43. Infrared divergences due to massless particles, Renormalisation and finite physical results Video
44. Symmetry constraints on Green's functions, Furry's theorem, Ward-Takahashi identity, Spontaneous breaking of gauge symmetry and superconductivity Video
45. Status of QED, Organisation of perturbative expansion, Precision tests Video