Simple Quantum Systems in Spacetimes with Closed Timelike Curves

TL;DR

This paper explores how quantum path integrals behave in spacetimes with closed timelike curves, showing that non-unitarity can occur but certain models remain unitary, highlighting the nuanced effects of such spacetimes on quantum amplitudes.

Contribution

It provides simple illustrative examples demonstrating the properties of quantum path integrals in spacetimes with closed timelike curves, including conditions for unitarity.

Findings

Non-relativistic potential scattering in CTC spacetimes can be non-unitary.

Hard sphere models in CTC spacetimes preserve unitarity.

Discrete models show exact unitarity despite CTC presence.

Abstract

Three simple examples illustrate properties of path integral amplitudes in fixed background spacetimes with closed timelike curves: non-relativistic potential scattering in the Born approximation is non-unitary, but both an example with hard spheres and the exact solution of a totally discrete model are unitary.