Introduction and scope, telescopes, distance and size measurements of astronomical objects, celestial mechanics, the Sun, planets, planet formation, interstellar medium, star formation, stellar structure, stellar evolution, star clusters - open clusters, globular clusters, the Milky-Way galaxy, nature of galaxies, normal and active galaxies, Newtonian cosmology, cosmic microwave background radiation, the early universe.

Special theory of relativity : Experimental background and postulates of the special theory, Lorentz transformation equations and their implications, space-time diagrams, Four vectors, tensors in flat space-time, relativistic kinematics and dynamics, relativistic electromagnetism. General theory of relativity : Principle of equivalence, gravitational red shift, geometry of curved spacetime, Einstein field equation, spherically symmetric solution of field equation.

Mathematical description of sound waves; physical sound production by vibrations in different dimensions; perception of music by the human ear and brain, the scientific meaning of psycho-acoustic concepts of pitch, loudness and timbre; Fourier analysis as a tool for characterizing timbre; musical scales, harmonics and tones; musical instruments with plucked, bowed and struck strings, wood-wind instruments, reed instruments and the human voice, percussions instruments such as tympani, and drums; engineering for sound reproduction in transducers, mikes, amplifiers and loudspeakers; sound spectrum analysis; basics of signal processing for electronic music production, filtration and enhancement; rudiments of room and auditorium acoustics ; hands-on work and projects.

Overview of Astronomy, Stellar and Galactic Astrophysics, Bremsstrahlung, Synchrotron radiation, free-free radiation, and Compton scattering, Radiative- transitions/line-emission, The radio sky and sources of radio signals, Theory of statistical random signals, Radio telescopes and Radio observations. Techniques of Line and continuum observations, Pulsar observations. Radio telescopes, antennas and receivers. Single dish and interferometric observations, Beam patterns, aperture synthesis and deconvolution, Phased arrays, Flux and Phase Calibration techniques. Study some radio telescopes GMRT, VLA, OWFA.

Introduction to lasers, theory of radiation, laser basics, optical resonators, longitudinal / transverse modes, pumping of laser media, Line broadening mechanism, Transient behaviour : Q-switching, mode locking, devices, techniques. Types of lasers : solid state lasers, gas lasers, liquid lasers, semiconductor laser, x-ray laser, free electron laser, maser. Non-linear optics: Phase matching, second harmonic generation, third harmonic generation, difference frequency generation, optical parametric generation etc. Applications of lasers : Industry, medicine, biology, optical /quantum communication, thermonuclear fusion, isotope separation, holography, laser cooling etc.

Klein-Gordon equation, SU(2) and rotation group, SL(2,C) and Lorentz group, antiparticles, construction of Dirac spinors, algebra of gamma matrices, Maxwell and Proca equations, Maxwell's equations and differential geometry; Lagrangian Formulation of particle mechanics, real scalar field and Noether's theorem, real and complex scalar fields, Yang-Mills field, geometry of gauge fields, canonical quantization of Klein-Gordon, Dirac and Electromagnetic field, spontaneously broken gauge symmetries, Goldstone theorem, superconductivity.

Klein-Gordon equation, time-dependent non-relativistic perturbation theory, spinless electron-muon scattering and electron-positron scattering, crossing symmetry, Dirac equation, standard examples of scattering, parity violation and V-A interaction, beta decay, muon decay, weak neutral currents, Cabbibo angle, weak mixing angles, CP violation, weak isospin and hypercharge, basic electroweak interaction, Lagrangian and single particle wave-equation, U(1) local gauge invariance and QED, non-Abelian gauge invariance and QCD, spontaneous symmetry breaking, Higgs mechanism, spontaneous breaking of local SU(2) gauge symmetry.

Review of relativistic mechanics, gravity as geometry, descriptions of curved space-time, tensor analysis, geodesic equations, affine connections, parallel transport, Riemann and Ricci tensors, Einstein’s equations, Schwarzschild solution, classic tests of general theory of relativity, mapping the universe, Friedmann- Robertson-Walker (FRW) cosmological model, Friedmann equation and the evolution of the universe, thermal history of the early universe, shortcomings of standard model of cosmology, theory of inflation, cosmic microwave background radiations (CMBR), baryogenesis, dark matter & dark energy.

Forces, energies, timescale and dimensionality in soft condensed matter, phase transition, mean field theory and its breakdown, simulation of Ising spin using Monte Carlo and molecular dynamics, colloidal dispersion, polymer physics, molecular order in soft condensed matter – i) liquid crystals ii) polymer, supramolecular self assembly.

Vacuum techniques, sample preparation techniques, X-ray diffraction, scanning probe microscopy, scanning electron microscopy, low temperature techniques, magnetic measurements, Mossbauer and positron annihilation spectroscopy, neutron diffraction, Rutherford backscattering, techniques in nuclear experimentation, high energy accelerators.

Schrodinger field theory (second quantized formalism), Bose and Fermi fields, equivalence with many body quantum mechanics, particles and holes, single particle Green functions and propagators, diagrammatic techniques, application to Fermi systems (electrons in a metal, electron – phonon interaction) and Bose systems (superconductivity, superfluidity).

Quantization of the electromagnetic field, single mode and multimode fields, vacuum fluctuations and zero-point energy, coherent states, atom - field interaction - semiclassical and quantum, the Rabi model, Jaynes-Cummings model, beam splitters and interferometry, squeezed states, lasers.

Symmetries, conservation laws and degeneracies; Discrete symmetries - parity, lattice translations and time reversal; Identical particles, permutation symmetry, symmetrization postulate, two-electron system, the helium atom; Scattering theory - Lippman- Schwinger equation, Born approximation, optical theorem, eikonal approximation, method of partial waves; Quantum theory of radiation - quantization of electromagnetic field, interaction of electromagnetic radiation with atoms; relativistic quantum mechanics

Basic concepts – group axioms and examples of groups, subgroups, cosets, invariant subgroups; group representation – unitary representation, irreducible representation, character table, Schur’s lemmas; the point symmetry group and applications to molecular and crystal structure; Continuous groups – Lie groups, infinitesimal transformation, structure constants; Lie algebras, irreducible representations of Lie groups and Lie algebras; linear groups, rotation groups, groups of the standard model of particle physics.

The Ising Model – Definition, equivalence to other models, spontaneous magnetization, Bragg- William approximation, Bethe- Peierls Approximation, one dimensional Ising model, exact solution in one and two dimensions; Landau’s mean field theory for phase transition – the order parameter, correlation function and fluctuation-dissipation theorem, critical exponents, calculation of critical exponents, scale invariance, field driven transitions, temperature driven condition, Landau-Ginzberg theory, two-point correlation function, Ginzberg criterion, Gaussian approximation; Scaling hypothesis – universality and universality classes, renormalization group; Elements of nonequilibrium statistical mechanics – Brownian motion, diffusion and Langevin equation, relation between dissipation and fluctuating force, Fokker-Planck equation

Review of Maxwell’s equations – Maxwell’s equations, scalar and vector potentials, gauge transformations of the potentials, the electromagnetic wave equation, retarded and advanced Green’s functions for the wave equation and their interpretation, transformation properties of electromagnetic fields; Radiating systems – multipole expansion of radiation fields, energy and angular momentum of multipole radiation, multipole radiation in atoms and nuclei, multipole radiation from a linear, centre-fed antenna; Scattering and diffraction – perturbation theory of scattering, scattering by gases and liquids, scattering of EM waves by a sphere, scalar and vector diffraction theory, diffraction by a circular aperture; Dynamics of relativistic particles and EM fields – Lagrangian of a relativistic charged particle in an EM field, motion in uniform, static electromagnetic fields, Lagrangian of the EM fields, solution of wave equation in covariant form, invariant Green’s functions; Collisions, energy loss and scattering of a charged particle, Cherenkov radiation, the Bremsstrahlung; Radiation by moving charges – Lienard-Wiechert potentials and fields, Larmor’s formula and its relativistic generalization; Radiation damping – radiative reaction force from conservation of energy, Abraham-Lorentz model.

Basics-Crystal structure, Wave Mechanics and the Schrodinger Equation, Free and Bound Particles, Fermi energy, Fermi-Dirac Statistics, Fermi level, Density of states, Band Theory of Solids, Concept of Band Gap, direct and indirect band gap, equation of motion, electron effective mass, concept of holes, Doping in semiconductors, Carrier transport - transport equations, Generation / Recombination Phenomena, Semiconductor processing and characterization, p-n junction, metal-semiconductor contacts, MOS capacitors, JFET, MESFET, MOSFET, Heterojunction devices, Quantum effect, nanostructures, Semiconductor and Spin Physics, Magnetic Semiconductors

Classical Information, probability and information measures, methods of open quantum systems using density operator formalism, quantum operations, Kraus operators. Measurement and information, Entropy and information, data compression, channel capacity, Resource theory of quantum correlations and coherence, and some current issues.

Manifolds, tensors, differential forms and examples from Physics, Riemannian geometry, relevance of topology to Physics, integration on a manifold, Gauss theorem and Stokes’ theorem using integrals of differential forms, fibre bundles and connections, applications of geometrical methods in Classical and Quantum Mechanics, Electrodynamics, Gravitation, and Quantum field theory. Rotations in real complex and Minkowski spaces laying group theoretical basis of 3-tensors and 4 tensors and spinors, transition from a discrete to continuous system, stress energy tensor, relativistic field theory, Noether’s theorem, tensor and spinor fields as representation of Lorentz group, action for spin-0 and spin-1/2, and super-symmetric multiplet, introduction of spin-1, spin-2 and spin-3/2 through appropriate local symmetries of spin-0 and spin-1/2 actions.

In this course, the nonlinear processes which take place during the interaction of light with matter will be studied in medium intensity (10 3 to 10 8 W/cm 2 ) to high and ultra- high intensity (10 9 to 10 21 W/cm 2 ) regimes. The nonlinear optics in the medium intensity regime in dielectric materials will cover basic concepts of nonlinear susceptibility, phase matching etc. and will discuss all major second order and third order non-linear effects. The high intensity laser-plasma interaction will cover processes of laser light absorption in plasma at high and ultra-high intensities, nonlinear processes in plasma, and light- matter interaction processes at ultra-high intensities. After studying the nonlinear physical processes happening in these intensity regions, four useful applications in four intensity regimes will be discussed.