Field theories with homogenous momentum space

TL;DR

This paper constructs a scalar field theory with a coset momentum space, revealing its dual in Snyder's non-commutative space-time, and introduces a non-associative star product that deforms Poincare symmetries.

Contribution

It presents a novel scalar field theory framework with coset momentum space and a non-associative star product in Snyder's space-time, expanding understanding of non-commutative geometries.

Findings

Dual scalar field theory in Snyder space-time

Star product realization of Snyder's non-commutative space

Deformation of Poincare symmetries in Snyder's framework

Abstract

We discuss the construction of a scalar field theory with momentum space given by a coset. By introducing a generalized Fourier transform, we show how the dual scalar field theory actually lives in Snyder's space-time. As a side-product we identify a star product realization of Snyder's non-commutative space, but also the deformation of the Poincare symmetries necessary to have these symmetries realized in Snyder's space-time. A key feature of the construction is that the star product is non-associative.