Quantum Field Theory in Spaces with Closed Time-Like Curves

TL;DR

This paper investigates quantum field theory in Gott spacetime with closed timelike curves, revealing non-unitarity and complex potentials, and analyzes the stress tensor near the Cauchy horizon.

Contribution

It constructs a scalar quantum field theory in a specific spacetime with closed timelike curves and analyzes its properties, including non-unitarity and stress tensor behavior.

Findings

Quantum field theory in this spacetime is non-unitary.

Particles can be created and annihilated in the acausal region, affecting probability conservation.

Stress tensor remains regular near the Cauchy horizon for small Compton wavelengths.

Abstract

Gott spacetime has closed timelike curves, but no locally anomalous stress-energy. A complete orthonormal set of eigenfunctions of the wave operator is found in the special case of a spacetime in which the total deficit angle is $2\pi$. A scalar quantum field theory is constructed using these eigenfunctions. The resultant interacting quantum field theory is not unitary because the field operators can create real, on-shell, particles in the acausal region. These particles propagate for finite proper time accumulating an arbitrary phase before being annihilated at the same spacetime point as that at which they were created. As a result, the effective potential within the acausal region is complex, and probability is not conserved. The stress tensor of the scalar field is evaluated in the neighborhood of the Cauchy horizon; in the case of a sufficiently small Compton wavelength of the field, the stress tensor is regular and cannot prevent the formation of the Cauchy horizon.