1.

Courses of Study (Physics)

The following courses are offered at the Centre:

a.

b.

c.

d.

e.

f.

g.

Courses Outline

PCO-801 Classical Mechanics

A quick review of Newton’s laws of motion, Inertial and non-inertial frames, Conservation laws, The harmonic oscillator, Forced oscillations and resonance, Many particle systems, Elastic and inelastic scattering, Motion of a rigid body, The independent coordinates of a rigid body, Orthogonal transformations, The Euler angles, The inertia tensor and its diagonalization, Euler’s theorem (on the motion of a rigid body), Motion of a symmetrical top, Central force motion, Gravitational field and elliptical orbits, Detailed discussion of Kepler’s Laws, Orbit precession, Coloumb’s Field and hyperbolic orbits,

Lagrangian, Variational principles, Euler-Lagrange equations, Constraints and their classifications, The Hamilton equations, Hamilton’s function and conservation theorem, Phase space trajectories, The principle of least action, Revisit of the Kepler’s problem, The virial theorem, Power law potentials, Infinitesimal rotations, The Coriolis force, The eigenvalues of the inertia tensor and the principal axis transformations, Torque free and Torque induced precession, Precession of the equinoxes, Small oscillations, Normal coordinates, Dissipative forces, Canonical transformation, Poisson Brackets and related topics, Liouville theorem, The Hamilton-Jacobi method, Lagrangian formulation for continuous systems, The stress-energy tensor and conservation theorems, Noether’s theorem.

Main Textbook:  

1.          Classical Mechanics (3^rd Edition), Herbert Goldstein, Charles Poole and John Safko, Addison Wesley; 3^rd Edition (January 15, 2002)

Go to Top

PCO-802 Methods of Mathematical Physics

A quick review of finite dimensional vector spaces, Eigenvalues and eigenvectors, Diagonalization.

Infinite dimensional linear spaces and corresponding linear operators, Hilbert spaces, Introduction to dual vectors and tensors, Summation convention, Inner and outer product, curvilinear coordinate tensors, Levi-Civita symbol, Symmetric and anti-symmetric tensors, Metric tensor and Christoffel symbols, Covariant derivative, Divergence, Laplacian and Curl.

Complex variables, Cauchy-Riemann conditions, Cauchy integral theorem, Cauchy’s integral formula, Laurent expansion, Singularities, Mappings, Residue theorem and calculus of residues with applications, Method of steepest descents, Analytic continuation, Several complex variables.

A quick review of group theory. Cayley’s theorem, Lagrange theorem, Group representations, Continuous groups, Generators, SO(3) and SU(2).

Main Textbook:  

1.       Essential Mathematical Methods for Physicists, G. Arfken and H. Weber, Academic Press; 1^st  Edition (August 8, 2003)

2.       Advanced Engineering Mathematics (9^th Edition), E. Kreyszig, John Wiley & Sons; 9^th Rev Edition (March 21, 2006)

3.       Mathematical Methods of Physics (2^nd edition), J. Mathews and R. Walker, Addison Wesley; 2^nd edition (January 11, 1971)

Go to Top

PCO-803 Quantum Mechanics

A review of Hilbert spaces, observables and completeness of eigenstates, Conjugate variables and canonical quantization, Schrodinger’s equation, Elementary examples of one-dimensional potentials and corresponding solutions of the Schrodinger equation, Probability and ensemble interpretation of the state vector, Heisenberg uncertainty principle, Elementary three dimensional potentials and corresponding solutions, Angular momentum, Eigenvalues of L² and L_z, Rotational invariance, The hydrogen atom.

Harmonic Oscillator with raising and lowering operators, Time independent perturbations, Harmonic oscillator with cubic and quartic potentials, Time dependent perturbations, Interaction of an atom with a radiation field, Spontaneous emission, Identical particles, Many-particle states and permutation symmetry, Completely symmetric and anti-symmetric states, The helium atom, Introduction to path integrals, Free particle propagator.

Main Textbook:

1.       The principles of quantum mechanics, P. A. M. Dirac, Clarendon Press; 4^th  edition  (1966)

2.       Principles of quantum mechanics (2^nd edition), R. Shankar, Springer; 2^nd edition 1994.

3.       Advanced quantum mechanics (3^rd edition), F. Schwabl, Springer; 3^rd edition (August 18, 2005)

Go to Top

PCO-804 Differential Equations (the same as MCO-804)

Systems of ordinary differential equations of the first order, Theory of ordinary differential equations of higher orders, Methods of solutions of boundary value problems for partial differential equations. Linear independence of functions and its use for solutions of linear equations, The Frobenius method, Solution of partial differential equations and boundary value problems by the separation of variables and by Fourier series and Laplace and Fourier transforms.

Main Textbook:

1.    Ordinary Differential Equations, I. G. Petrovski, Dover Publications Inc.; New Ed edition (September 3, 1973)

2.       Advanced Engineering Mathematics, E. Kreyszig, Wiley; 9^th Sol Mn edition (October 6, 2006)

3.       Advanced Engineering Mathematics, D. Zill and M. Cullen, Jones & Bartlett Pub; 3^rd edition (February 17, 2006)

Go to Top

PCO-805 Electromagnetism

A quick review of Coulomb’s law, Motion in the Coulomb field, electrostatics, Boundary value problems, Moments and systems of charges in an external field, Magnetostatics, Magnetic moments, Maxwell’s equations.

Michaelson-Morley experiment and the constancy of the speed of light, Equivalence of inertial frames and Lorentz transformations, Velocity addition, Minkowski space and the four-vector formalism, Lorentz invariance, The null cone, The electromagnetic field tensor, Action of the EM field, The variational principle and the Maxwell equations, The four potential, Gauge invariance, The continuity equation, The energy momentum tensor of EM field, Electromagnetic waves, Green’s functions, Radiation from point and extended sources, Radiation reaction.

Main Textbook:

1.       Classical electrodynamics (3^rd edition), J. Jackson, Wiley; 3^rd edition (August 10, 1998)

2.       The classical theory of fields (4^th edition), L. Landau and E. Lifshitz, Pergamon Press (1975)

Go to Top

PCO-806 Thermal Physics

A quick review of the laws of thermodynamics, Thermodynamic potentials, Relations between the derivatives of thermodynamic quantities, Connection between thermodynamics and statistical mechanics.

The Maxwell-Boltzmann distribution, the Boltzmann equation and the ideal gas. The Fermi and Bose distributions, Ensembles, Polyatomic gases, Equilibrium, Phase space, Phase diagrams and critical points, Fluctuations with Gaussian distribution, Spatial correlations of density fluctuations, Phase transitions, Order parameter and kinds of Phase transitions, Critical phenomena.

Main Textbook:

1.       Statistical Mechanics” (2^nd edition), R. K. Pathria, Butterworth-Heinemann; 2^nd edition (July 23, 1996)

2.       Statistical Physics (3^rd edition), L. Landau and E. Lifshitz, Butterworth-Heinemann; 3^rd  edition (April 1984)

Go to Top

PCO-807 Advanced Quantum Mechanics

Discussion of the properties of Hilbert space, Spectra of Hamiltonians and related topics, Creation and annihilation operators and Fock space for bosons and fermions, The Fermi sphere and excitations, Fermi and Bose distributions, Degenerate electron gas and Bose condensates, Introduction to relativistic quantum mechanics via the Klein Gordon equation, Free solutions of the Klein Gordon equation, Dirac equation, Dirac matrices and their properties, Non-relativistic limit, Lorentz invariance of Dirac equation and transformation of spinors, Transformation of bilinear forms, Free particle solutions, Canonical quantization, Covariant derivative and coupling with the electromagnetic field.

Main Textbook:

1.       Advanced Quantum Mechanics” (3^rd edition), F. Schwabl, Springer; 3^rd edition (August 18, 2005)

2.       Quantum Theory: A wide spectrum, E. Manoukian, Springer; 1^st edition (November 20, 2006)

3.       Advanced Quantum Mechanics, J.J. Sakurai, Addison Wesley (January 11, 1967)

Go to Top

PQT-801 Quantum Field Theory – I

Quick review of Classical Field Theory (if required), Symmetries and Noether’s theorem, Introduction to Quantum Field Theory via quantization of Klein-Gordon Fields, Need for spin half fields and quantization of Dirac Fields, Quantization of Maxwell’s Fields, Interaction picture, Feynman diagrams, Some elementary processes in quantum electrodynamics, Renormalization in quantum electrodynamics.

Main Textbook:

1.       Quantum Field Theory, F. Mandl and G. Shaw, Wiley; Rev Sub edition (December 1993)

2.       A First Book of Quantum Field Theory, P. B. Pal and A. Lahiri, CRC; 2 edition (September 2, 2005)

3.       An Introduction to Quantum Field Theory, M. E. Peskin and D. V. Schroeder, HarperCollins Publishers (June 1995)

4.       A Modern Introduction to QFT, M. Maggiore, Wiley; Rev Sub edition (December 1993)

5.       Quantum Field Theory: A Modern Perspective,          V. P. Nair, Oxford University Press, USA (February 10, 2005)

Go to Top

PQT-802 Foundations of Quantum Mechanics

Mathematical formalism of quantum mechanics: Hilbert space, Dirac notation, Hermitian operators, Eigenvectors, eigenvalues, spectral theorem, position and momentum operators, The projection postulate, trace of an operator The density operator, mixed states, Unitary operators in quantum theory, Time-independent perturbation theory: non-degenerate and degenerate cases, Time-dependent perturbation theory: Dyson series, transition probabilities Tensor product of Hilbert spaces, quantum entanglement, EPR and the incompleteness of quantum theory. Bell inequalities, quantum non-locality, Kochen-Specker and Gleason theorems, Measurement problem in quantum theory, Everett's many-worlds interpretation, DeBroglie-Bohm interpretation, Ghirardi-Rimini-Weber dynamic reduction model, Quantum information theory, quantum state teleportation.

Main Textbook:

1.       Quantum Mechanics II, Martin Plenio, http://www.lsr.ph.ic.ac.uk/~plenio/teaching.html.

2.       Lectures on Quantum Theory: Mathematical and Structural Foundations, Chirs J. Isham, Imperial College Press 1995

Go to Top

PQT-901 Quantum Field Theory – II (Pre-Requisite: PQT-801)

Functional path integrals, Quantization of non-abelian gauge theories, Radiative corrections, Renormalization and Renormalization group, Higgs field and spontaneous symmetry breaking, Detailed discussion of the Standard Model of particle physics, Anomalies.

Main Textbook:

1.       An Introduction to Quantum Field Theory, M. E. Peskin and D. V. Schroeder, Harper Collins Publishers (June 1995)

2.       The Quantum Theory of Fields, Vol. 1 and 2, S. Weinberg, Cambridge University Press (August 13, 1996)

3.       Renormalization Methods: A Guide for Beginners, McComb, Oxford University Press, USA; 1^st edition (January 6, 2008)

Go to Top

PQT-902 Quantum Field Theory – III (Pre-Requisite: PQT-901)

Path Integrals for fermions, Supersymmetry, Non-perturbative methods, Quantum Fields in curved background, Horizons and the Hawking effect, Applications in cosmology and astrophysics.

Main Textbook:

An Introduction to Quantum Field Theory

M. E. Peskin and D. V. Schroeder

HarperCollins Publishers (June 1995)

Textbooks:

1.       The Quantum Theory of Fields, Vol. 3, S. Weinberg, Cambridge University Press; 1 edition (February 24, 2000)

2.       Introduction to Quantum Fields in Curved Spacetime and the Hawking Effect, Jacobson, arXiv:gr-qc/0308048

3.       Quantum fields in Curved space, N. Birrell and P. Davies, Cambridge University Press (April 27, 1984)

Go to Top

PHE-801 Particle Physics I

Brief summary of quantum Fields (if required), Introduction to fundamental particles (quarks and leptons), forces and gauge bosons, Interactions of particles, Discrete and continuous symmetries, Conservation laws, Scattering of leptons with leptons, SU(3) of color (Quark model) and confinement, Weak interactions, CP violation, Introduction to the Standard Model of Particle Physics.

Main Textbook:

1.       Introduction to High Energy Physics, D. Perkins, Cambridge University Press; 4 edition (April 24, 2000)

2.       Quarks and Leptons: An Introductory Course in Modern Particle Physics, Francis Halzen and Alan D. Martin, Wiley (January 1984)

3.       A modern introduction to particle physics, Riazuddin and Fayyazuddin, World Scientific Publishing Company; 2^nd Rev Sub edition (September 29, 2000)

Go to Top

PHE-901 Particle Physics II (Pre-Requisite: PHE-801)

Detailed discussion of neutrino physics including neutrino oscillations and neutrino masses, The standard model of particle interactions: QCD and asymptotic freedom, Deep inelastic scattering and partons, Electroweak unification and its experimental consequences, Higgs phenomenology, Composite Higgs, Discussion of Grand unification including SU(5) and SO(10), Supersymmetry, Kaluza-Klein theories and applications in cosmology.

Main Textbook:

1.       Introduction to High Energy Physics, D. Perkins, Cambridge University Press; 4th Edition (April 24, 2000)

2.       Quarks and Leptons: An Introductory Course in Modern Particle Physics, Halzen and Martin, Wiley (January 1984)

3.       Unification and Supersymmetry, The Frontiers of Quark-Lepton Physics, (3^rd Edition),      R. Mohapatra, Springer-Verlag; 2^nd edition (January 1992)

Go to Top

PHE-902 Group Theory for Physicists

Introduction to Lie groups and Lie algebras, Internal SU(n) symmetries and their representations especially using tensor methods and Young's tableaux, Spacetime symmetries using Lorentz and Poincaré group and their representations, Conformal group, Introduction to supersymmetric algebra.

Main Textbook:

1.    Kinematics and symmetries, Giovani Costa et al

2.    Chapter 16 of Mathematical Methods of Physics” (2^nd Edition), by J. Mathews and R. Walker, Addison Wesley; 2nd Edition (January 11, 1971)

3.       Group Theory, Riazuddin and Fayyazuddin

Go to Top

PRP-801 General Relativity (the same as MMP-811)

(Candidates for the thrust area of Relativistic Physics will have to take MCO-803 Geometry as well.)

Review of the history of mechanics and dynamics. Review of the history of mechanics and dynamics continued. Original formulation of Special Relativity; velocity addition; 3-d formulation. 4-vector formalism; Poincare group; the null cone. Applications of relativity in mechanics and use of 4-vector formulation of electromagnetism. Special Relativity with small accelerations. Fundamentals of classical field theory. Relativistic fields and the stress energy tensor. The principles of General Relativity and experimental evidence for them. Geodesic deviation and the Einstein equations. The Newtonian limit of Relativity. The Schwarzschild exterior solution and relativistic equations of motion

The classical tests of Relativity and their current status. Relativity as a field theory of gravity. The Schwarzschild interior solution. The Reissner-Nordstrom (RN) metric The Kerr-Newman metric. Linearized gravity and gravitational waves Foliations. Tidal forces and the pseudo-Newtonian formalism Black holes: coordinate and essential singularities, horizons, coordinates passing through horizons. The Kruskal and the Carter-Penrose (CP) diagrams for the Schwarzschild geometry. The maximal extension The Einstein-Rosen bridge. Wormholes. The CP diagram for the RN metric. The no-hair and cosmic censorship hypotheses Gravitational forces about black holes. Black hole thermodynamics. Observational status and central black holes. Isometries, homotheties and their significance in Relativity. Conformal transformations and the Weyl tensor

Main Textbook:

1.          General Relativity, R. Wald, University Of Chicago Press (June 15, 1984)

Go to Top

PRP-911 Cosmology I

Cosmological Principle, RW metric, Friedmann Equations and solutions, Red-shift, Horizons, Big Bang Model of the universe and the expanding universe, Thermal history of the universe, Contents of the universe, their contribution to the total energy density of the universe and their evolution, Evidence for dark matter and its properties, Cosmic Microwave Background, Primordial nucleosynthesis, Small inhomogeneities in the RW background and structure formation, SN-Ia observations and dark energy, Problems of the standard Model, Inflation.

Main Textbook:

1.       Modern Cosmology,S. Dodelson, Academic Press; 1 Edition (March 7, 2003)

2.       Principles of Physical Cosmology, P. Peebles, Princeton University Press (April 19, 1993)

Go to Top

PRP-912 Cosmology  II (Pre-Requisite: PHE-911)

Detailed discussion of Structure formation, CDM-Lambda model and alternatives, Possible candidates for the dark matter, Possible interpretations of dark energy, Large extra dimensions in cosmology, Baryon asymmetry and baryogenesis, The early universe and quantum gravity, The origin of density perturbations.

Main Textbook:

1.       Modern Cosmology, S. Dodelson, Academic Press; 1 Edition (March 7, 2003)

2.       Principles of Physical Cosmology, P. Peebles, Princeton University Press (April 19, 1993)

PRP-914 Two-Component Spinor Formalism (the same as MMP-912)

Go to Top

Spinors as vectors of the complex representation space of SO(2n).  Two-component spinors as vectors of the complex representation of the Lorentz group. The algebra of two-component spinors using the abstract index notation. The Pauli matrices as a basis for spinor representations. The geometrical representation of spinors. Use of spinors for dealing with thee Riemann, Ricci and Weyl tensors. Spin coefficients and the Newman_Penrose equations. Principal null directions, the Petrov classification and the Segrè classification in terms of spinors.

Main Textbook:

1.       Adam’s Prize Essay, Roger Penrose, Cambridge University

2.       Brandeis Summer School Vol.1: Lectures on General Relativity, A. Trautman /F.A.E. Pirani/ H. Bondi, Prentice Hall 1965 (Chapter: F.A.E. Pirani, Introduction to Gravitational Radiation Theory pp. 249 – 373)

3.       The Theory of Spinors, Elie Cartan, M.I.T. Press 1966

4.       Exact Solutions of Einstein’s Equations (Second Edition), Hans Stefani, Dietrich Kramer, Malcolm A.H. MacCallum, Cornelius Hoenselaers and Eduard Herlt, Cambridge University Press 2003

Go to Top

PRP-915 Twistor Theory

Review of two-component spinors, their geometry, algebra and calculus (as given in the first textbook). Review of complex analysis, complex geometry, complex methods and cohomology theory for discussing physical phenomena (as given in the third textbook). The laws of physical phenomena and a review of Relativity, Quantum Theory, Thermodynamics and Cosmology. The algebra, geometry and calculus of Twistors. Attempts to localize twisters and the use of twistor cohomology for massless fields. Null congruences and null twistors. Classification of curvature tensors. Conformal infinity and the Bondi-Metzner-Sachs group.

Main Textbook:

1.       Spinors and Space-Time, Vol. I, Two-Spinor Calculus and Relativistic Fields, R. Penrose & W. Rindler, Cambridge University Press, Cambridge 1984.

2.       Spinors and Space-Time, Vol. II, Spinor and Twistor Methods in Space-Time Geometry, Roger Penrose, Cambridge University Press, Cambridge 1986

3.       The Road to Reality: A Complete Guide to the Laws of the Universe, R. Penrose, A. Knopf 2001

Go to Top

PRP-917 Relativistic Astrophysics (Same as MMP-913)

Fundamentals of thermodynamics. The kinetic theory of gases and statistical mechanics. Integral theorems on stellar equilibrium. Isothermal and polytropic spheres. Radiation and equations of equilibrium. The virial theorem. The Hertzsprung-Russell diagram. Stellar models. Quantum statistics. Degenerate Fermi gases, white dwarfs and neutron stars.

Main Textbook:

1.       An Introduction to the Theory of Stellar Structure, S. Chandrasekhar, Dover 1967

2.       Elementary Statistical Physics, C. Kittel, John Wiley and Sons 1964

3.       Physics and Contemporary Needs Vol.1, Remo Ruffini, (Atricle by) Astrophysics, General Relativity and Cosmology,(Edited By Riazuddin), Plenum Press 1977

4.       Physics and Contemporary Needs Vol.6, (Article by) Carl Rouse, Stellar Structure and Stellar Evolution --- Another View (Editors) A. M. Khan, S. Riazuddin, Asghar Qadir and M.N. Kazi, Plenum Press 1983

Go to Top

PRP-919 Supermassive Black Holes

The course has been divided into three parts. The first part deals with the galactic structure which involves the evolution and dynamics of galaxies. The second part will focus on the stellar and gas dynamics/ processes near the central black hole of Milky Way galaxy, Sgr A*. Study of the parameters and dynamical models of the central black hole. Techniques of studying the supermassive black hole via gravitational lensing and gravitational waves. The third part deals with the study of active galactic nuclei and quasars as possible hosts of supermassive black holes.

Main Textbook:

1.       Galactic Dynamics, J. Binney and S. Tremaine, University Press (1987).

2.       Astrophysics of the Galactic Central Regions (PhD Thesis), A. Nucita, Universita Degli Studi Di Lecce (2004) or University of Lecce, Italy.

Go to Top