Unruh effect of nonlocal field theories with a minimal length

TL;DR

This paper investigates how nonlocal field theories with a minimal length, inspired by doubly special relativity, modify the Unruh effect, showing corrections due to Lorentz violations but recovering standard results in the Lorentz-invariant limit.

Contribution

It introduces a generic nonlocal model with minimal length that allows Lorentz violations and calculates the resulting modifications to the Unruh effect.

Findings

Unruh effect is corrected by minimal length effects in nonlocal theories.

In the Lorentz-invariant limit, the Unruh effect matches the local theory.

Modified Wightman function reflects nonlocality and minimal length effects.

Abstract

The nonlocal field theory commonly requires a minimal length, and so it appears to formulate the nonlocal theory in terms of the doubly special relativity which makes the speed of light and the minimal length invariant simultaneously. We set up a generic nonlocal model having the same set of solutions as the local theory but allowing Lorentz violations due to the minimal length. It is exactly corresponding to the model with the modified dispersion relation in the doubly special relativity. For this model, we calculate the modified Wightman function and the rate of response function by using the Unruh-DeWitt detector method. It turns out that the Unruh effect should be corrected by the minimal length related to the nonlocality in the regime of the doubly special relativity. However, for the Lorentz-invariant limit, it is shown that the Wightman function and the Unruh effect remain the same as those of the local theory.