P304 Special Theory of Relativity

Course No: 
  1. Physics before relativity – 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
  2. 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
  3. 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, hydrodynamics and electrodynamics as tensor equations
  4. 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.
  5. 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: 
  1. Introduction to Special Theory of Relativity by Resnick
  2. Relativity by A. Einstein
  3. Classical Electrodynamics by J.D. Jackson
  4. Electrodynamics by Panofsky and Phillips
  5. Classical Mechanics by Goldstein
  6. GTR and Cosmology by Weinberg
  7. Lecture notes in NISERwiki (also at phatak) 
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