Relativistic Quantum Mechanics

IISc Bangalore Course , Prof. Apoorva D Patel

Lecture 1: Introduction, The Klein-Gordon equation

Download:    MP4,FLV & 3GP
Lecture Details :

Relativistic Quantum Mechanics by Prof. Apoorva D Patel,Department of Physics,IISc Bangalore.For more details on NPTEL visit

Course Description :

KLEIN-GORDON AND DIRAC EQUATIONS: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;LORENTZ AND POINCARE GROUPS: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

QUANTUM ELECTRODYNAMICS: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

Other Resources

These lecture videos are delivered by IISc Bangalore, under the NPTEL program, lot of nptel video courses are available for learning online.

COURSE Reviews

5 Stars 10
4 Stars 5
3 Stars 0%
2 Stars 4
1 Stars 7
3.3 Overall Ratings