Quantum fields on timelike curves

TL;DR

This paper investigates the conditions under which quantum fields can be smeared with singular test functions supported on timelike curves, extending the understanding of quantum fields along such curves and defining a form of time-translation.

Contribution

It demonstrates that quantum fields satisfying the micro local spectrum condition can be smeared with certain singular distributions on timelike curves, generalizing space-time translations in Minkowski space.

Findings

Quantum fields can be smeared with singular test functions on timelike curves.

Defined a generalized time-translation along timelike curves for free fields.

Extended the framework of quantum field theory to include singular smearing along timelike paths.

Abstract

A quantum field F(x) exists at an event x of space-time in general only as a quadratic form. Only after smearing with a smooth test function we get an operator. In this paper the question is considered whether it is possible as well to smear F(x) with a singular test function T (i.e. a test distribution) supported by a smooth timelike curve. It is shown that this is always possible if F(x) satisfies the micro local spectrum condition and T belongs to a special class of distributions which retain some regularity in timelike directions. In the free field case these results are used to define some kind of time-translation along the curve which generalizes global space-time translations of Minkowski space.