Quantum field theory on the degenerate Moyal space

Abstract

We prove that the self-interacting scalar field on the four-dimensional degenerate Moyal plane is renormalisable to all orders when adding a suitable counterterm to the Lagrangean. Despite the apparent simplicity of the model, it raises several non trivial questions. Our result is a first step towards the definition of renormalisable quantum field theories on a non-commutative Minkowski space.

arXiv comment21 pages, 4 figures. We use the techniques of the previous version in a conclusive manner on the degenerate Moyal space

Cited by in corpus (10)

• Quantum gauge theories on noncommutative 3-d space
• Slavnov-Taylor identities, non-commutative gauge theories and infrared divergences
• Worldline approach to noncommutative field theory
• On the Renormalization of Non-Commutative Field Theories
• Inferring the covariant $\Theta$-exact noncommutative coupling in the top quark pair production at linear colliders
• Matrix Model Fixed Point of Noncommutative Phi-Four
• Constructive Renormalization of the $2$-dimensional Grosse-Wulkenhaar Model
• Degenerate noncommutativity
• Renormalization of the commutative scalar theory with harmonic term to all orders
• Wilson RG of Noncommutative ${\Phi }_4^4$