# Quantum field theory in generalised Snyder spaces

## TL;DR

This paper explores a generalized Snyder model incorporating all Lorentz-invariant deformations of the Heisenberg algebra, analyzing its algebraic structure, momentum addition, star product, and scalar field theory, revealing equivalence to commutative theories.

## Contribution

It introduces a comprehensive generalization of the Snyder model, extending noncommutative geometry with Lorentz invariance and analyzing its implications for quantum field theory.

## Key findings

- The generalized model maintains Lorentz invariance.
- The star product and momentum addition laws are derived perturbatively.
- Scalar field theory on these spaces is equivalent to the commutative case.

## Abstract

We discuss the generalisation of the Snyder model that includes all possible deformations of the Heisenberg algebra compatible with Lorentz invariance and investigate its properties. We calculate peturbatively the law of addition of momenta and the star product in the general case. We also undertake the construction of a scalar field theory on these noncommutative spaces showing that the free theory is equivalent to the commutative one, like in other models of noncommutative QFT.