Field theory amplitudes in a space with SU(2) fuzziness

TL;DR

This paper explores the structure of field theory amplitudes in a three-dimensional noncommutative space with SU(2) fuzziness, focusing on constructing observables and handling delta distributions, with explicit scalar field examples.

Contribution

It introduces a framework for analyzing transition amplitudes in SU(2) noncommutative space and addresses subtleties in defining conservation laws within this context.

Findings

Explicit scalar field amplitude calculations in lowest order perturbation

Clarification of delta distribution treatment in noncommutative geometry

Framework for constructing observables in SU(2) fuzzy space

Abstract

The structure of transition amplitudes in field theory in a three-dimensional space whose spatial coordinates are noncommutative and satisfy the SU(2) Lie algebra commutation relations is examined. In particular, the basic notions for constructing the observables of the theory as well as subtleties related to the proper treatment of $\delta$ distributions (corresponding to conservation laws) are introduced. Explicit examples are given for scalar field theory amplitudes in the lowest order of perturbation.