Some Consequences of Invariance under Charge Conjugation
- L . WoL, D . G . RAvENHALL
We study the non relativistic limit of the charge conjugation operation C in the context of the Dirac equation coupled to an electromagnetic field. The limit is well defined and, as in the relativistic case, C, P (parity) and T (time reversal) are the generators of a matrix group isomorphic to a semidirect sum of the dihedral group of eight elements and Z2. The existence of the limit is supported by an argument based in quantum field theory. Finally, if one complexifies the Lorentz group and therefore the galilean spacetime xμ, then the explicit form of the matrix for C allows to interpret it, in this context, as the complex conjugation of the spatial coordinates: ~x → ~x. This result is natural in a fiber bundle description.