Snyder Geometry and Quantum Field Theory

TL;DR

This paper explores how Snyder geometry modifies translational invariance in quantum field theory, leading to momentum-dependent symmetry and new formulations for localized states and Feynman rules.

Contribution

It introduces a modified translational invariance in Snyder geometry, enabling the construction of localized states and Feynman rules in the quantum field theory framework.

Findings

Translational invariance becomes momentum-dependent in Snyder geometry.

Maximally localized states can be constructed within this modified framework.

New Feynman rules are derived for the quantum field theory with Snyder geometry.

Abstract

We find that, in presence of the Snyder geometry, the notion of translational invariance needs to be modified, allowing a momentum dependence of this symmetry. This step is necessary to build the maximally localized states and the Feynman rules of the corresponding quantum field theory.