Quantum complex scalar field in two-dimensional spacetime with closed timelike curves and a time-machine problem

Abstract

The quantum complex scalar field which obeys the authomorphic condition in the two-dimensional spacetime with closed timelike curves and the chronology horizon is considered. The renormalized stress - energy tensor is obtained. It is shown that the value of the stress - energy tensor is regular at the chronology horizon for specific authomorphic parameters. Thus the particular example of a field configuration is given for which the Hawking's chronology protection conjecture is violated.