Course Code

P304

Credit

8

Total Hours

42 Lectures + 14 Tutorials

Outcome of the Course

Trains the student in basic and advanced concepts in special relativity and introduces the basic ideas up on which General relativity is based on. Also provides in depth training in applications of group theory in relativity. Prepares the student for studying general relativity in future.

Approval

Syllabus

- Review: Galilean relativity, Newtonian mechanics, Electrodynamics and inconsistency with Galilean relativity, ether and experiments for its detection, failure to detect ether. Measurement of velocity of light in moving frames. Lorentz, Poincare and developments towards relativity
- Einstein’s special theory: Constancy of velocity of light as a postulate. Derivation of Lorentz transformation. Length contraction and time dilation. Mass- energy relation, Doppler shift. Minkowski space-time diagram, boosts as complex rotations in Minkowski space
- Four dimensional space-time continuum, Lorentz transformations as coordinate transformations, vectors, scalar product, scalars, tensors, contravariant and covariant objects, laws of physics as tensor equations, Mechanics, hydro-dynamics and electrodynamics as tensor equations
- Beyond special relativity: Inertial and gravitational mass, Equivalence principle, Introducing gravitational field as general coordinate transformation, Principle of general covariance, Metric tensor and affine connection, Gravitational potential as metric tensor, Laws of physics in presence of gravitation, gravitational time dilation and red shift, Experimental observation of gravitational red shift
- Lorentz and Poincare groups: abelian and non-abelian groups, Rotations in two and three dimensions, generators of rotations, Representations (finite dimensional), Casimir operators, Lorentz transformations as a group, Generators for translations, rotations and boosts, Finite and infinite dimensional representations

Reference Books

- Introduction to Special Theory of Relativity by Resnick
- Relativity by A. Einstein
- Classical Electrodynamics by J.D. Jackson
- Electrodynamics by W. K. H. Panofsky & M. Phillips
- Classical Mechanics by H. G oldstein
- GTR and Cosmology by S. Weinberg
- Classical Theory of Fields by L. Landau & E. Lifshitz