# Bohmian Field Theory on a Shape Dynamics Background and Unruh Effect

## TL;DR

This paper demonstrates the existence of Unruh radiation within Bohmian field theory formulated on a shape dynamics background, revealing radiation effects without relying on traditional Lorentz symmetry or spacetime structure.

## Contribution

It introduces a novel approach to Unruh radiation analysis using Bohmian field theory on a shape dynamics background, bypassing conventional spacetime assumptions.

## Key findings

- Proved Unruh radiation exists in this non-Lorentz-invariant setting.
- Showed the interaction Hamiltonian is real due to the real metric quantities.
- Detected Unruh radiation using an Unruh-DeWitt detector without standard spacetime.

## Abstract

In this paper, we investigate the Unruh radiation in the Bohmian field theory on a shape dynamics background setting. Since metric and metric momentum are real quantities, the integral kernel to invert the Lichnerowicz-York equation for first order deviations due to existence of matter terms turns out to be real. This fact makes the interaction Hamiltonian real. On the other hand, the only contribution to guarantee the existence of Unruh radiation has to come from the imaginary part of the temporal part of the wave functional. We have proved the existence of Unruh radiation in this setting. It is also important that we have found the Unruh radiation via an Unruh-DeWitt detector in a theory where there is no Lorentz symmetry and no conventional space-time structure.