Symmetries of noncommutative scalar field theory

TL;DR

This paper explores the symmetries of noncommutative scalar field theory on Moyal space, showing how orthogonal invariance can be maintained at quantum level by specific symplectic structure restrictions.

Contribution

It demonstrates that orthogonal symmetry in noncommutative scalar field theory can be preserved quantum mechanically through particular symplectic structure choices.

Findings

Classical action invariant under orthogonal group with symplectic action

Quantum invariance achieved by restricting to a specific symplectic orbit

Identifies conditions for symmetry preservation in noncommutative field theory

Abstract

We investigate symmetries of the scalar field theory with harmonic term on the Moyal space with euclidean scalar product and general symplectic form. The classical action is invariant under the orthogonal group if this group acts also on the symplectic structure. We find that the invariance under the orthogonal group can be restored also at the quantum level by restricting the symplectic structures to a particular orbit.