Causality in noncommutative spacetime

TL;DR

This paper addresses causality issues in the DFRA noncommutative spacetime framework by analyzing scalar fields, demonstrating algebraic properties, and solving the Klein-Gordon equation with Green functions, advancing quantum field theory in this setting.

Contribution

It proves that the DFRA algebra follows canonical commutation relations and provides solutions to the Klein-Gordon equation in noncommutative spacetime, facilitating quantum field theory development.

Findings

DFRA algebra obeys canonical commutation relations

Solutions to Klein-Gordon equation with Green functions are constructed

First step towards quantum field theory in DFRA noncommutative spacetime

Abstract

In this paper we investigated the causality problem present in the recent work about the Doplicher-Fredenhagen-Roberts-Amorim (DFRA) noncommutative framework which analyzed the complex scalar field. To accomplish this task we provided a brief review of the main ingredients of the problem and we demonstrated precisely that the DFRA algebra obeys the rules of the Canonical Commutation Relations algebra. This fact permitted us to prove the form of the DFRA operators previously constructed in the usual way. After that, we introduced the solution of its Klein-Gordon equation with a source term. Its solution was accomplished through the retarded, advanced and causal Green functions constructed in this noncommutative ten dimensional DFRA spacetime. We believe that this solution constitutes the first step in the elaboration of a quantum field theory using the DFRA formalism where the noncommutative parameter is an ordinary coordinate of the system and therefore has a canonical conjugate momentum.