Course

Unit 1

Classical Mechanics and Relativity: Galilean Relativity, Newtonian Mechanics, Electrodynamics and Galilean Relativity, Ether, Michelson–Morley experiment, Attempts by Lorentz & Poincare.

Unit 2

Special Theory of Relativity: Einstein’s postulates, Lorentz’s transformation, Length contraction, Time dilation. Relativistic Kinematics, Doppler shift, Minkowski Diagrams, Boosts and Minkowski space.

Unit 3

Four dimensional Space-Time geometry: Space-time continuum, Lorentz transformations as coordinate transformations, tensors, contravariant and covariant objects, four vectors.
Relativistic Dynamics: Four velocity, Four momentum, Four acceleration, Relativistic Collisions, Conservation of four-momentum, Equivalence of Mass and Energy. Central force problem in relativity.

Unit 4

Electromagnetic Theory in covariant form: Maxwell’s equations in covariant form, Four dimensional vector potential, Energy-Momentum Tensor and Conservation Laws, Lagrangian formulation of Electrodynamics, Radiation.

Unit 5

Covariant formulation Fluid Dynamics: Perfect fluids, Pressure and proper density, Energy-Momentum tensor, Relativistic Euler equations, Equation of state, Speed of sound.
The Lorenz & Poincare groups: The Lorentz and Poincare algebras and their representations.
The Principle of Equivalence and preamble to General Theory of Relativity.

Prerequisites: Mechanics & Electrodynamics

Course Objectives: To have a comprehensive physical idea and mathematical understanding of Special theory of Relativity and its applications in Electrodynamics, Fluid Dynamics etc using four-dimensional covariant analysis.

Text Books

1. N. M. J. Woodhouse, Special Theory of Relativity, Springer, 2003.
2. Steven Weinberg, Gravitation and Cosmology: Principles and Applications of the General Theory of Reactivity, Wiley India, 2008.

Reference Books

1. Landau & Lifshitz, Classical Field Theory, University Science Books, 1E, 2004.
2. Ashok Das, Lectures on Electromagnetism, Hindustan Book Agency – World Scientific, 2013.
3. A. Einstein, Relativity: The Special and the General Theory.