Minimal Electromagnetic Interaction andC,TNoninvariance

Abstract

It is well known that the principle of minimal electromagnetic interaction determines a unique electromagnetic-interaction form for a spin-0 or spin-\textonehalf{} charged particle. In this paper, it is shown that the same principle, when applied to a spin-1 charged particle, leads to a minimal electromagnetic interaction that depends on two arbitrary real parameters: the charge and the magnetic moment. It is further shown that the minimal electromagnetic interaction of a system of $N$ spin-1 particles of the same charge depends on the charge $\ensuremath{\epsilon}$ and an ($N\ifmmode\times\else\texttimes\fi{}N$) Hermitian matrix, called the magnetic-moment matric $M$. Such a minimal electromagnetic interaction can be noninvariant under $C$ and $T$. The general condition of $C$, $T$ invariance, or non-invariance is analyzed. These considerations are extended to a system of $N$ neutral spin-1 particles, assuming that the minimal electromagnetic interaction of such a system is not zero. Application to the observed ${\ensuremath{\varphi}}^{0}$, ${\ensuremath{\rho}}^{0}$, and ${\ensuremath{\omega}}^{0}$ particles gives a $C$, $T$ noninvariant minimal electromagnetic interaction, which, however, is invariant under $P$ and $\mathrm{CT}$. By making a further assumption concerning its transformation property under $S{U}_{3}$, this $C$, $T$ noninvariant interaction assumes a simple and unique form. Some of its experimental consequences are discussed.