Quantum fields on timelike curves

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.