Noether's Theorem, Canonical Quantization of Scalar Fields, Massive Electromagnetism, Propagators, Dyson Expansion, Feynman Diagrams, Dirac Fields, Path Integral Formalism, Bosonic and Fermionic Path Integrals.
Special Relativity, Metrics and Tensors, Manifold, Co-variant Derivative and Parallel Transport, Riemann Curvature Tensor, Equivalence Principle, Stress-Energy Tensor, Einstein's Field Equations.
Classical and statistical probability, Random variables, probability distributions, Law of large numbers, Central limit theorem, Micro-canonical, canonical and grand canonical ensembles, Maxwell-Boltzmann, Bose-Einstein and Fermi-Dirac statistics, Blackbody radiation, Debye solid and Fermi gas, Bose-Einstein condensates, Ising Model, Phase transitions and critical exponents.
Scalar and Vector Potentials, Method of Images, Multipole Expansion, Electromagnetic Plane Waves, Charged Particles in Plane Waves, Radiation, Multipole Radiation, Scattering.
Uncertainties, Scientific Report Writing, Data Acquisition and Processing through LabView, Temperature Oscillations in a Metal: Probing Aspects of Fourier Analysis, Measuring Muon Lifetime.