Chronology protection and quantized fields: Complex automorphic scalar field in Misner space

Abstract

The renormalized stress-energy tensor 〈Tμν〉 of the quantized complex massless scalar field which obeys the automorphic condition in Misner space is obtained. It is shown that there exists a special value of the automorphic parameter for which 〈Tμν〉 is regular on the chronology horizon, and so cannot act as a protector of chronology through a backreaction on a spacetime metric. However, it is shown that, at the same time, the value of the absolute square of the field 〈φφ̄〉, which characterizes the quantum field fluctuations, is divergent on the chronology horizon.