Possible New Form of SpontaneousTViolation

In (2+1)-dimensional models with a Chern-Simons term, there is a periodicity in the parameter $\frac{e^2}{2\mu }$, where $e$ is the smallest charge in the theory and $\frac{\mu }{2}$ is the coefficient of the Chern-Simons term. Since $\mu \to -\mu$ under the action of time reversal $T$, in such a theory the question of $T$ invariance becomes involved with the dynamical issue of what are the allowable values of the charge. We show how cross sections develop $T$-violating terms for "forbidden" values of the charge. Connections are made with some recent ideas concerning the mechanism of high-temperature superconductivity.