Unruh-Fulling effect in nonlocal field theory: The role of Unruh decomposition

TL;DR

This paper explores the Unruh-Fulling effect within nonlocal field theories using Unruh quantization, revealing that the effect's temperature remains universal despite modifications in detector response and number operator expectations.

Contribution

It introduces the use of Unruh quantization in nonlocal theories and compares Lorentz invariant and noninvariant cases, highlighting the universality of the Unruh temperature.

Findings

In Lorentz noninvariant theories, the number operator and detector response are multiplicatively modified.

In Lorentz invariant theories, the Unruh effect remains identical to the standard case.

The Unruh temperature remains unchanged in both Lorentz invariant and noninvariant nonlocal theories.

Abstract

We investigate the Unruh-Fulling effect in a class of nonlocal field theories by examining both the number operator and Unruh-DeWitt detector methods. Unlike in previous literature, we use Unruh quantization to quantize the matter field. Such choice, as oppose to standard Minkowski decomposition, naturally incorporates the time translational invariance in the positive frequency Wightman function and thus captures the thermal equilibrium of the system. We analyze the Unruh-Fulling effect for a massless real scalar field in both the Lorentz noninvariant and Lorentz invariant nonlocal theories. In Lorentz noninvariant nonlocal theory, the expectation value of number operator and the response function of the detector are modified by an overall multiplicative factor. Whereas in Lorentz invariant nonlocal theory these quantities remain identical to those of the standard Unruh-Fulling effect. The temperature of the thermal bath remains unaltered for both the Lorentz noninvariant and Lorentz invariant nonlocal theories. Therefore, in terms of temperature, the nonlocal Unruh-Fulling effect is universal while it is derived via Unruh quantization, whereas the transition rate may be modified.