The abstract [formula omitted] and [formula omitted] groups of discrete [formula omitted] and T symmetries

Abstract

Essential symmetry properties of physical quantities of classical mechanics and classical electromagnetism can be rationalized via the Abelian symmetry group GPT, with four operations (identity E, space inversion P, time reversal T, and combined PT) isomorphic to the spatial C2v point group. To account for charge conjugation C, a larger discrete group, GCPT, with eight operations (E,P,T,C, and their products, CP,CT,PT, and CPT), isomorphic to the spatial D2h point group, has been considered. Some features of these groups are discussed by a few examples, showing in particular that they provide group-theoretical implications for the existence of magnetic monopoles, magnetic scalar potential, magnetic charge density and magnetic current density, and magnetic-field induced electronic anapoles. A set of linearly independent vectors belonging to a representation space is constituted by eight fermion bilinears of quantum field theory. The GCPT group can be used to determine the discrete symmetry properties of molecular response tensors and provides interesting elucidations of established notions in a different, group-theoretical light, e.g., new understanding of duality transformations, which leave the Maxwell equations invariant, and a geometrical reinterpretation of Barron’s concept of true enantiomers.