Relativistic Quantum Mechanics
Relativistic Quantum Mechanics. Instructor: Prof. Apoorva D. Patel, Department of Physics, IIT Bangalore. This course covers topics on relativistic quantum mechanics: Dirac and KleinGordon equations, Lorentz and Poincare groups, Fundamental processes of Quantum Electrodynamics.
This is a course on relativistic quantum mechanics. Relativity, specifically special relativity, and quantum mechanics have been two very highly successful theories of our twentieth century. And what this subject amounts to is combining the two theories in a very successful manner and working out the predictions. Relativity essentially follows from the property that speed of light in vacuum is an invariant quantity. And mathematically, that is extended to the principle of the Lorentz transformations. Quantum mechanics tells that nature is discrete at a small scale and its formulation is based on unitary evolution of quantities known as wave functions or states. These two theories have been successful on their own. Relativistic quantum mechanics is just on the border line of merging relativity and quantum mechanics, and it offers many consequences as a result. This course will explore those consequences.
(from nptel.ac.in)
KleinGordon and Dirac Equations 
Lecture 01  Introduction, the KleinGordon Equation 
Lecture 02  Particles and Antiparticles, Two Component Framework 
Lecture 03  Coupling to Electromagnetism, Solution of the Coulomb Problem 
Lecture 04  BohrSommerfeld Semi Classical Solution of the Coulomb Problem, The Dirac Equation and the Clifford Algebra 
Lecture 05  Dirac Matrices, Covariant Form of the Dirac Equation, Equations of Motion, Spin, Free Particle Solutions 
Lecture 06  Electromagnetic Interactions, Gyromagnetic Ratio, Lorentz Force, Larmor Precession 
Lecture 07  The Hydrogen Atom Problem, Symmetries, Parity, Separation of Variables 
Lecture 08  The Frobenius Method Solution, Energy Levels and Wavefunctions 
Lecture 09  Nonrelativistic Reduction, The FoldyWouthuysen Transformation 
Lecture 10  Interpretation of Relativistic Corrections, Reflection from a Potential Barrier 
Lecture 11  The Klein Paradox, Pair Creation Process and Examples 
Lecture 12  Zitterbewegung, Hole Theory and Antiparticles 
Lecture 13  Charge Conjugation Symmetry, Chirality, Projection Operators, The Weyl Equation 
Lecture 14  Weyl and Majorana Representations of the Dirac Equation, Unitary and Antiunitary Symmetries 
Lecture 15  Time Reversal Symmetry, The PCT Invariance 
Lecture 16  Arrow of Time and Particleantiparticle Asymmetry, Band Theory for Graphene 
Lecture 17  Dirac Equation Structure of Low Energy Graphene States, Relativistic Signatures in Graphene Properties 
Lorentz and Poincare Groups 
Lecture 18  Groups and Symmetries, the Lorentz and Poincare Groups 
Lecture 19  Group Representations, Generators and Algebra, Translations, Rotations and Boosts 
Lecture 20  The Spinor Representation of SL (2, C), The Spinstatistics Theorem 
Lecture 21  Finite Dimensional Representations of the Lorentz Group, Euclidean and Galilean Groups 
Lecture 22  Classification of One Particle States, The Little Group, Mass, Spin and Helicity 
Lecture 23  Massive and Massless One Particle States 
Lecture 24  P and T Transformations, Lorentz Covariance of Spinors 
Lecture 25  Lorentz Group Classification of Dirac Operators, Orthogonality and Completeness of Dirac Spinors, Projection Operators 
Quantum Electrodynamics 
Lecture 26  Propagator Theory, Nonrelativistic Case and Causality 
Lecture 27  Relativistic Case, Particle and Antiparticle Contributions, Feynman Prescription and the Propagator 
Lecture 28  Interactions and Formal Perturbative Theory, The Smatrix and Feynman Diagrams 
Lecture 29  Trace Theorems for Products of Dirac Matrices 
Lecture 30  Photons and the Gauge Symmetry 
Lecture 31  Abelian Local Gauge Symmetry, the Covariant Derivative and Invariants 
Lecture 32  Charge Quantization, Photon Propagator, Current Conservation and Polarizations 
Lecture 33  Feynman Rules for Quantum Electrodynamics, Nature of the Perturbative Expansion 
Lecture 34  Dyson's Analysis of Perturbation Series, Singularities of the Smatrix, Elementary QED Processes 
Lecture 35  The Tmatrix, Coulomb Scattering 
Lecture 36  Mott Crosssection, Compton Scattering 
Lecture 37  KleinNishina Result for CrossSection 
Lecture 38  Photon Polarisation Sums, Pair Production through Annihilation 
Lecture 39  Unpolarised and Polarised CrossSections 
Lecture 40  Helicity Properties, Bound State Formation 
Lecture 41  Bound State Decay, Nonrelativistic Potentials 
Lecture 42  Lagrangian Formulation of QED, Divergences in Green's Functions, Superficially Divergent 1loop Diagrams and Regularization 
Lecture 43  Infrared Divergences due to Massless Particles, Renormalization and Finite Physical Results 
Lecture 44  Symmetry Constraints on Green's Functions, Furry's Theorem, WardTakahashi Identity, Spontaneous Breaking of Gauge Symmetry and Superconductivity 
Lecture 45  Status of QED, Organization of Perturbative Expansion, Precision Tests 
Related Links 
Relativistic Quantum Mechanics
Instructor: Prof. Apoorva D. Patel, Department of Physics, IIT Bangalore. This course covers topics on relativistic quantum mechanics: Dirac and KleinGordon equations, Lorentz and Poincare groups, Fundamental processes of Quantum Electrodynamics.
