Two-point functions with an invariant Planck scale and thermal effects

TL;DR

This paper proposes a novel deformation of two-point functions in field theory that incorporates an invariant Planck scale, analyzing its effects on detector responses in various spacetime backgrounds.

Contribution

It introduces a new method of deforming two-point functions directly, preserving symmetries and incorporating the Planck scale, offering an alternative to modified dispersion relations.

Findings

Deformed two-point functions depend on the Planck length.

Modified response functions show observable effects at the Planck scale.

The approach preserves fundamental symmetries of the underlying theory.

Abstract

Nonlinear deformations of relativistic symmetries at the Planck scale are usually addressed in terms of modified dispersion relations. We explore here an alternative route by directly deforming the two-point functions of an underlying field theory. The proposed deformations depend on a length parameter (Planck length) and preserve the basic symmetries of the corresponding theory. We also study the physical consequences implied by these modifications at the Planck scale by analyzing the response function of an accelerated detector in Minkowski space, an inertial one in de Sitter space, and also in a black hole spacetime.