Chronology Protection and Quantized Fields: Complex Automorphic Scalar Field in Misner Space

Abstract

The renormalized stress-energy tensor $⟨T_{\mu \nu }⟩$ 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 $⟨T_{\mu \nu }⟩$ 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 $⟨{\varphi }^2⟩$, 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.

7 pages, LaTeX, two figures are available in PCX or postscript format upon request, to appear in Proceedings of the 3rd Friedmann Seminar

References in corpus (3)

• Cosmic Strings and Chronology Protection
• Quantum Field Theory in Spaces with Closed Time-Like Curves
• Quantum Complex Scalar Field in the Two-Dimensional Spacetime with Closed Timelike Curves and a Time-Machine Problem

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