Quantum fields on closed time-like curves

TL;DR

This paper extends the Deutsch model of closed time-like curves to quantum fields, analyzing how different quantum states interact with CTCs and how the model transitions to standard quantum mechanics as CTC size varies.

Contribution

It generalizes the Deutsch model to quantum fields using the equivalent circuit formalism, including various quantum states and the transition to normal quantum mechanics.

Findings

Model behaves like a quantum feedback loop when CTC is small

Interaction with coherent, squeezed, and single-photon states analyzed

Transition to standard quantum mechanics as CTC size decreases

Abstract

Recently, there has been much interest in the evolution of quantum particles on closed time-like curves (CTCs). However, such models typically assume point-like particles with only two degrees of freedom - a very questionable assumption given the relativistic setting of the problem. We show that it is possible to generalise the Deutsch model of CTCs to fields using the equivalent circuit formalism. We give examples for coherent, squeezed and single-photon states interacting with the CTC via a beamsplitter. The model is then generalised further to account for the smooth transition to normal quantum mechanics as the CTC becomes much smaller than the size of the modes interacting on it. In this limit, we find that the system behaves like a standard quantum mechanical feedback loop.