中国科学院大学で行った講義(学部4年生向け)の補足資料など

Lectures on relativistic quantum mechanics
(@UCAS 2019-10)

Contents

  • Why the Dirac/Weyl/Majorana equations?
  • Dirac equation
    • -From Dirac to Pauli
    • Heuristic approach: From Klein-Gordon to Dirac
  • Dirac Hamiltonian
    • From Dirac to Pauli
    • -Non-relativistic limit 1
    • -Non-relativistic limit 2: Foldy-Wouthuysen-Tani transformation
  • Represantations
    • 2dim rotation by vector representation
    • 2dim rotation by 1dim complex representation
    • 3dim rotation by vector representation
    • 3dim rotation by spinor representation
    • 1+1 dim “rotation” = Lorentz boost
    • Lorentz transformation as a Jacobi matrix
  • Lorentz covariance
    • The Dirac equation in covariant form
    • Maxwell’s equation in the covariant form
  • Dirac Lagrangian and the local U(1) gauge symmetry
    • Maxwell’s equation
    • Dirac Lagrangian
  • Relativistic equations from the group theoretical approach
    • Undotted and dotted spinors
    • The Weyl equation
    • The Dirac equation
    • The Majorana equation
  • From special relativity to general relativity
    • The covariant derivative and the affine connection
    • The tetrad and the spin connection
  • Dirac equation in a rotating frame
    Appendix: The Christoffel symbol from the variation principle