Introduction:
Galilean transformation and invariance
of Newton's laws of motion, non-invariance of Maxwell's equations.
Michelson-Morley experiment and explanation of the null result.
Special Theory of Relativity:
Concept of inertial frame. Postulates of special theory; simultaneity; Lorentz transformation along one of the axes – length contraction, time dilatation and velocity addition theorem, Fizeau’s experiment. Four vectors. Relativistic dynamics : variation of mass with velocity; energy momentum relationship.
Vectors and Tensors:
Covariant and contravariant vectors.
Contraction. Covariant, contravariant, and mixed tensors of rank-2, transformation
properties. The metric tensor (flat space-time only). Raising and lowering of
indices with metric tensors. (Consistent use of any one convention ---
diag(-1,1,1,1) or diag(1,-1,-1,-1).) Example of common four-vectors: position,
momentum, derivative, current density, four-velocity.
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