Syllabus

Module-1 (5 hours)

The Lorentz and Poincare groups, group representations, generators and algebra,
Translations, rotations and boosts, Massive and massless one particle states, P and T transformations,

Module-2 (12 hours)

KLEIN-GORDON AND DIRAC EQUATIONS: Introduction, The Klein-Gordon equation
Particles and antiparticles, Feynman-Stueckelberg Interpretation, The Dirac equation and the Clifford algebra, Dirac matrices, Covariant form of the Dirac equation, Charge conjugation symmetry, Chirality, Projection operators, Lorentz covariance of spinors, Lorentz group classification of Dirac operators, Bilinear covariants, Orthogonality and completeness of Dirac spinors, Projection
operators

Module-3 (6 hours)

The Weyl equation, Weyl and Majorana representations of the Dirac equation, Unitary and antiunitary symmetries, Time reversal symmetry, The CPT invariance, Arrow of time and particle-antiparticle asymmetry,

Module-4 ( 8 hours)

Equations of motion, Spin, Free particle solutions, Electromagnetic interactions, Gyromagnetic ratio, Coupling to electromagnetism, Solution of the Coulomb problem, The Hydrogen atom problem, Symmetries, Parity, Separation of variables ,The Frobenius method solution, Energy levels and wavefunctions,

Module-5 (6 hours)

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.

To impart knowledge on
1. Importance of Lorentz transformations of relativistic equations
2. Formulation of relativistic Quantum Mechanics
3. Non-relativistic limit of relativistic equations and their applications

At the end of course, students will be able to:
CO1: Understand the difference between relativist and non-relativist formulation of quantum Mechanics
CO2: Understand the difference between particles of integral and half-integral spins such as elementary particles.
CO3: Acquire the knowledge of working with fundamental particles and their dynamics

J. J. Sakurai, Advanced Quantum Mechanics, Pearson Education, 2007.

J.D. Bjorken and S.D. Drell,, Relativistic Quantum Mechanics: with Applications in Condensed Matter &Atomic Physics, McGraw-Hill (1964)

M.E. Peskin and D.V. Schroeder,, An Introduction to Quantum Field Theory, Addison-Wesley (1995)

S. Weinberg, The Quantum Theory of Field Volume 1:The Foundations,, Cambridge University Press (1995).Imperial College Press, 1998