# Nonlinear Field Space Theory and Quantum Gravity

## TL;DR

This paper introduces a novel framework extending field theories to nonlinear phase spaces, revealing quantum gravity-like effects such as algebra deformations and modified uncertainty relations.

## Contribution

It proposes the first extension of field theories to nonlinear phase spaces and demonstrates its implications through a scalar field model with spherical phase space.

## Key findings

- Algebra deformations similar to quantum gravity effects
- Generalized uncertainty relations
- Shifted vacuum energy predictions

## Abstract

Phase spaces with nontrivial geometry appear in different approaches to quantum gravity and can also play a role in e.g. condensed matter physics. However, so far such phase spaces have only been considered for particles or strings. We propose an extension of the usual field theories to the framework of fields with nonlinear phase space of field values, which generally means nontrivial topology or geometry. In order to examine this idea we construct a prototype scalar field with the spherical phase space and then study its quantized version with the help of perturbative methods. As the result we obtain a variety of predictions that are known from the quantum gravity research, including algebra deformations, generalization of the uncertainty relation and shifting of the vacuum energy.