# On thermal field fluctuations in ghost-free theories

## TL;DR

This paper investigates how non-local ghost-free modifications to quantum field theories affect thermal fluctuations and the fluctuation-dissipation relation, providing explicit formulas and analyzing the impact of non-locality.

## Contribution

It derives explicit expressions for thermal fluctuations in ghost-free theories and explores how non-locality alters fluctuation amplitudes and the fluctuation-dissipation theorem.

## Key findings

- Non-locality modifies the amplitude of thermal fluctuations.
- Explicit thermal Hadamard function is obtained for static delta-potential.
- Discussion of fluctuation-dissipation theorem in ghost-free theories.

## Abstract

We study the response of a scalar thermal field to a $\delta$-probe in the context of non-local ghost-free theories. In these theories a non-local form factor is inserted into the kinetic part of the action which does not introduce new poles. For the case of a static $\delta$-potential we obtain an explicit expression for the thermal Hadamard function and use it for the calculation of the thermal fluctuations. We then demonstrate how the presence of non-locality modifies the amplitude of these fluctuations. Finally, we also discuss the fluctuation-dissipation theorem in the context of ghost-free quantum field theories at finite temperature.