Astroparticle Physics
Detection techniques, gamma-ray astronomy, X-ray astronomy, dark matter, neutrino physics, big bang nucleosynthesis, cosmic inflation, cosmic rays, galactic magnetic fields, supernovae, pulsars, gamma-ray bursts, supernova remnants, active galactic nuclei.
Classical Mechanics
Newton's Laws, Lagrangian Mechanics, Hamiltonian Mechanics, variational principles, symmetries and conservation Laws, Hamilton-Jacobi theory, dynamical systems, nonlinear dynamics, chaos theory, classical field theory.
Cosmology
Observational cosmology, cosmological principle, FLRW metric, Friedmann equations, cosmological models, big bang theory, inflationary cosmology, early universe dynamics, dark matter, dark energy, structure formation, baryogenesis, primordial nucleosynthesis, gravitational lensing.
Electromagnetism
Electrostatics, dielectrics, Laplace's equation, multipole expansion, magnetostatics, electrodynamics, Maxwell's equations, radiation, electromagnetic fields and matter, electromagnetic interactions, covariant formulation.
General Relativity
Special relativity, Minkowski spacetime, tensor analysis, curved spacetime, Einstein's field equations, Schwarzschild solution, black holes, gravitational waves, Penrose diagrams, Kerr solution, black hole thermodynamics, Hawking radiation, Oppenheimer-Snyder collapse, nature of singularities.
Mathematical Methods for Physics
Complex analysis, vector calculus, variational calculus, linear algebra, tensor algebra, group theory, differential equations, integral transforms, special functions, probability and statistics, stochastic processes, numerical analysis.
Quantum Computing
Qubits, quantum gates, quantum algorithms, quantum error correction, quantum simulation, quantum cryptography, quantum machine learning, quantum annealing, optimization algorithms, topological quantum computing, quantum complexity theory, quantum hardware, quantum information theory.
Quantum Field Theory
Classical field theory, canonical quantization, scalar field theory, Klein-Gordon equation, Feynman propagator, S-Matrix, interacting fields, Wick's theorem, Feynman diagrams, renormalization, quantum electrodynamics, gauge symmetries, spontaneous symmetry breaking, electroweak theory, quantum chromodynamics, path integral formulation, effective field theory, anomalies, solitons, instantons, supersymmetry, string theory, quantum gravity.
Quantum Mechanics
Schrodinger's equation, hydrogen atom, postulates, spin, bosons, fermions, Pauli exclusion principle, perturbation theory, Rayleigh-Ritz method, Wigner-Weyl transformation, WKB approximation, Klein-Gordon equation, Dirac equation, covariant formulation.
Statistical Physics
Entropy, ideal gas, Maxwell-Boltzmann distribution, partition function, canonical ensemble, quantum statistics, Fermi-Dirac statistics, Bose-Einstein statistics, Bose-Einstein condensation, Fermi gas, Debye model, Ising model
Thermal Physics
Laws of thermodynamics, temperature, heat, thermal equilibrium, work, energy conservation, heat capacity, heat engines, refrigerators, Carnot cycle, efficiency, entropy, reversible processes, thermodynamic potentials, phase transitions, ideal gas laws, kinetic theory of gases, solids, irreversible processes, blackbody radiation.