Noncommutative Complex Scalar Field and Casimir Effect

TL;DR

This paper constructs a noncommutative complex scalar field model, solves its equations, and analyzes the Casimir effect, revealing a small noncommutativity-induced repulsive force that modifies the Casimir potential.

Contribution

It introduces a noncommutative scalar field framework with deformed commutation relations and explores its impact on the Casimir effect, providing new insights into quantum field behavior under noncommutativity.

Findings

Noncommutativity induces a repulsive force at microscopic scales.

The Casimir potential is modified with a minimum at a specific point.

Vacuum energy calculated to second order in noncommutativity parameter.

Abstract

A noncommutative complex scalar field, satisfying the deformed canonical commutation relations proposed by Carmona et al. [27]-[31], is constructed. Using these noncommutative deformed canonical commutation relations, a model describing the dynamics of the noncommutative complex scalar field is proposed. The noncommutative field equations are solved, and the vacuum energy is calculated to the second order in the parameter of noncommutativity. As an application to this model, the Casimir effect, due to the zero point fluctuations of the noncommutative complex scalar field, is considered. It turns out that in spite of its smallness, the noncommutativity gives rise to a repulsive force at the microscopic level, leading to a modifed Casimr potential with a minimum at the point amin= racine(5/84){\pi}{\theta}.