Quantization of Noncommutative Scalar Solitons at finite $\theta$

TL;DR

This paper investigates quantum corrections to noncommutative scalar solitons, specifically Q-balls and GMS solitons, highlighting UV/IR mixing effects and their implications in (2+1) dimensions.

Contribution

It extends the analysis of noncommutative scalar solitons by quantizing them and examining quantum corrections, revealing UV/IR mixing phenomena.

Findings

Quantum corrections exhibit UV/IR mixing effects.

UV divergences are present in Q-balls but absent in GMS solitons.

Quantization near the commutative limit provides insights into soliton stability.

Abstract

We start by discussing the classical noncommutative (NC) Q-ball solutions near the commutative limit, then generalize the virial relation. Next we quantize the NC Q-ball canonically. At very small theta quantum correction to the energy of the Q-balls is calculated through summation of the phase shift. UV/IR mixing terms are found in the quantum corrections which cannot be renormalized away. The same method is generalized to the NC GMS soliton for the smooth enough solution. UV/IR mixing is also found in the energy correction and UV divergence is shown to be absent. In this paper only (2+1) dimensional scalar field theory is discussed.