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
- 2dim rotation by
- 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