Notes on Special Theory of Relativity

• 01
  Tensors
  • Transformations
  • Summation convention
  • Metric, and Contravariant and covariant vectors
  • Transformations that keep the distance invariant
  • Problems
    Probelms on tensors from Arfken
  
  
• 02
  Position 4-vector and Gradient 4-vector
  • Lorentz transformations
  • Space time diagrams
  • Time dilation
  • 4-velocity
  • Velocity addition
  • Problems
    Proving vector identites using indices
    • Space time diagram
    • Time dilation
    • Velocity addition
  
  
• 03
  Relativistic kinematics
  • Energy momentum tensor
    • Nonrelativistic limit of kinetic energy
  • Massless particles (photons)
    • Doppler shift
  • General boost transformation
  • Problems
    Space time concept
    • 4-velocity
    • 4-momentum
    • 4-acceleration
    • Non-relativistic limits
  
  
• 04
  Motion in 1-D with constant acceleration
  • Length contraction
  • Collisions
    • Decay of a particle
    • Comption scattering
    • Pair creation
    • Theshold energy (zero momentum frame)
  • Problems
    Non-relativistic motion in 1D with constant acceleration
    • Collisions
  
  
• 05
  4-acceleration
  • 4-Force
  • Motion in 1-D with constant proper acceleration
  • Problems
    4-acceleration
    • Problems
  
  
• 06
  Maxwell's equations in 4-vector notation
  • Electromagnetic force on relativistic particles
  • Relativistic particle in a constant magnetic field
  • Problems
    Maxwell's equations
    • Problems
  
  
• 07
  Motion in a constant electric field (and non-relativistic limits)
  • Transformation of E and B
  • Problems (in 2 files)
    Invariants in terms of field tensor
    • Determination of eigen values of field tensor
    • Motion of a relativistic particle in a constant electric field initially at rest
    • Problems from Landau and Lifshitz