Consistent Construction of Perturbation Theory on Noncommutative Spaces

TL;DR

This paper investigates how non-local deformations in noncommutative spaces affect the construction of perturbation theory, revealing discrepancies with traditional approaches especially when time is involved, and extends analysis to scalar and gauge fields.

Contribution

It provides a detailed analysis of the impact of non-local deformations on interaction point time ordered perturbation theory in noncommutative quantum field theories, highlighting key discrepancies.

Findings

Discrepancies between IPTOPT and path integral approach in noncommutative spaces.

Analysis of scalar and gauge field models under non-local deformations.

Clarification of the role of the free Hamiltonian in noncommutative theories.

Abstract

We examine the effect of non-local deformations on the applicability of interaction point time ordered perturbation theory (IPTOPT) based on the free Hamiltonian of local theories. The usual argument for the case of quantum field theory (QFT) on a noncommutative (NC) space (based on the fact that the introduction of star products in bilinear terms does not alter the action) is not applicable to IPTOPT due to several discrepancies compared to the naive path integral approach when noncommutativity involves time. These discrepancies are explained in detail. Besides scalar models, gauge fields are also studied. For both cases, we discuss the free Hamiltonian with respect to non-local deformations.