A general discussion of the physical interpretation of this operator in terms of electrical charge is given in the article on charge conjugation. Additional discussions are provided by Bjorken & Drell or Itzykson & Zuber. In more abstract terms, it is the spinorial equivalent of complex conjugation of the U ( 1 ) coupling of the electromagnetic field. This can be seen as follows. If one has a single, real scalar field, it cannot couple to electromagnetism; however, a pair of real scalar fields, arranged as a complex number, can. For scalar fields, charge conjugation is the same as complex conjugation. The discrete symmetries of the U ( 1 ) gauge theory follows from the "trivial" observation that