  The renormalized stress-energy tensor $\langle T_{\mu\nu}\rangle$ of the
quantized complex massless scalar field which obeys the automorphic condition
in Misner space is obtained. It is shown that there exists the special value of
the automorphic parameter for which $\langle T_{\mu\nu}\rangle$ is regular on
the chronology horizon and, so, can not act as a protector of chronology
through a back reaction on a spacetime metric. However, it is shown that, at
the same time, the value of field square $\langle\phi^2\rangle$, which
characterizes the quantum field fluctuations, is divergent on the chronology
horizon. The assumption is suggested that the infinitely growing quantum field
fluctuations, which appear if a (self)interaction of the scalar field is taken
into account, would prevent the chronology horizon formation.
