Some Consequences of Invariance under Charge Conjugation

Abstract

The charge conjugation operator, which transforms charged fields to their charge-conjugate fields and reverses the sign of the electromagnetic field, is explicitly constructed. States of zero net charge are eigen-states of this operator; the eigenvalues are ${\mathrm{}(-1\mathrm{})\mathrm{}}^n$ for states of $n$ photons and (+1) and (-1) for the singlet and triplet $S$ states of positronium, respectively. The effect of charge conjugation on neutral boson fields is also discussed. Physical consequences of the invariance of field theory under this transformation include: 1. For usual interactions a spin-zero particle (including the singlet $S$ state of positronium) cannot decay into three photons, although this decay is shown to be allowed by angular momentum and parity considerations. 2. The $m=1\mathrm{}$ and $m=-1\mathrm{}$ levels of triplet positronium cannot be split by a magnetic field.