- #1
jjustinn
- 164
- 3
The first thing you learn about the Dirac equation is that it provides a relativistically-correct quantum-mechanical description of spin-1/2 charged particles, e.g. the electron.
Then, it seems that it's at least implied that the Dirac equation completely describes the interaction between multiple Dirac particles (e.g. electron-electron)...
However, I don't think I've ever seen it spelled out explicitly like this (from Houghty - Lagrangian Interaction):
So am I reading that correctly? Do the Maxwell equations literally follow from the Dirac equation? I've seen them put together in coupled equations of motion (e.g. the Dirac current = source for Maxwell field, Maxwell field = external potential for Dirac field), but I always took those as empirical rather than necessary deductive fact...
Then, it seems that it's at least implied that the Dirac equation completely describes the interaction between multiple Dirac particles (e.g. electron-electron)...
However, I don't think I've ever seen it spelled out explicitly like this (from Houghty - Lagrangian Interaction):
In its application to the U(1) phase symmetry of [Dirac particles] one finds that the mediating field of the interaction ... is precisely the one described by Maxwell's equations. The fact that the interaction is mediated by only one real vector field, whose quantized particle is the photon, is a consequence of there being only one real parameter (the phase angle) in the global symmetry group.
So am I reading that correctly? Do the Maxwell equations literally follow from the Dirac equation? I've seen them put together in coupled equations of motion (e.g. the Dirac current = source for Maxwell field, Maxwell field = external potential for Dirac field), but I always took those as empirical rather than necessary deductive fact...