Remark on charge conjugation in the non relativistic limit

Details Remark on charge conjugation in the non relativistic limit Remark on charge conjugation in the non relativistic limit

2005-04-27

arxiv.org/abs/hep-th/0504223v2

Int.J.Theor.Phys. 45 (2006) 1965-1976

Physics

High Energy Physics

High Energy Physics - Theory

8 pages

Scientific paper

10.1007/s10773-006-9166-4

We study the non relativistic limit of the charge conjugation operation $\cal C$ in the context of the Dirac equation coupled to an electromagnetic field. The limit is well defined and, as in the relativistic case, $\cal C$, $\cal P$ (parity) and $\cal T$ (time reversal) are the generators of a matrix group isomorphic to a semidirect sum of the dihedral group of eight elements and $\Z_2$. The existence of the limit is supported by an argument based in quantum field theory. Also, and most important, the limit exists in the context of galilean relativity. Finally, if one complexifies the Lorentz group and therefore the galilean spacetime $x_\mu$, then the explicit form of the matrix for $\cal C$ allows to interpret it, in this context, as the complex conjugation of the spatial coordinates: $\vec{x} \to \vec{x}^*$. This result is natural in a fiber bundle description.

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