Symmetries of noncommutative scalar 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.

12 pages, revised version

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Cited by in corpus (12)

• Quantum gauge theories on noncommutative 3-d space
• $\kappa$-Poincaré invariant quantum field theories with KMS weight
• Gauge theories on quantum spaces
• Exact Partition Functions for Gauge Theories on ${\mathbb{R}}_{\lambda }^3$
• Noncommutative gauge theories on ${\mathbb{R}}_{\lambda }^3$: Perturbatively finite models
• On the Origin of the Harmonic Term in Noncommutative Quantum Field Theory
• Involutive representations of coordinate algebras and quantum spaces
• Translation-Invariant Noncommutative Renormalization
• Spectral theorem in noncommutative field theories: Jacobi dynamics
• Renormalization of the commutative scalar theory with harmonic term to all orders
• Quantum spaces, central extensions of Lie groups and related quantum field theories
• Noncommutative Supergeometry and Quantum Supergroups