Quantum fields on timelike curves

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