Theory of Spin-½ Particles with Parity-Nonconserving Interactions

It is shown that when interactions are not invariant under parity conjugation, both the self-mass term ($-\delta m\overline{\psi }\psi$) and the term ($-\frac{a\overline{\psi }{\gamma }_{\mu }{\gamma }_5\partial \psi }{\partial x_{\mu }}$) are induced by the self-interaction of any spin-½ particle with nonvanishing mass. (For simplicity $T$ invariance is assumed.) When $a^2>1\mathrm{}$, the spin-½ particle propagates in vacuum faster than the velocity of light. When $a^2=1\mathrm{}$, the observed mass should be zero. Therefore, it follows that $a^2<1\mathrm{}$ for any spin-½ particle with nonvanishing mass. Since $1>\mathrm{}{a}^2>\frac{1}{3}$ implies the existence of ghost states, one must require $a^2<~\frac{1}{3}$. Although $a$ has no physical meaning for free particles, as an example, it is also shown that it has a physical meaning when a charged particle is interacting with an external electromagnetic field. The value of $a$ is estimated for the electron and the muon.