Induced Gauge Theory on a Noncommutative Space

Abstract

We discuss the calculation of the 1-loop effective action on four dimensional, canonically deformed Euclidean space. The theory under consideration is a scalar ${\varphi }^4$ model with an additional oscillator potential. This model is known to be re normalisable. Furthermore, we couple an exterior gauge field to the scalar field and extract the dynamics for the gauge field from the divergent terms of the 1-loop effective action using a matrix basis. This results in proposing an action for noncommutative gauge theory, which is a candidate for a renormalisable model.

8 pages

References in corpus (15)

• Heat kernel expansion: user's manual
• The Spectral Action Principle
• Gauge Theory on Noncommutative Spaces
• Renormalisation of ϕ^4-theory on noncommutative R^4 in the matrix base
• Duality in Scalar Field Theory on Noncommutative Phase Spaces
• Renormalization of noncommutative phi 4-theory by multi-scale analysis
• Noncommutative gauge theory for Poisson manifolds
• Induced Gauge Theory on a Noncommutative Space
• The spectral action for Moyal planes
• Non-commutative heat kernel
• Trouble with space-like noncommutative field theory
• Generalized Yang-Mills actions from Dirac operator determinants
• Heat kernel, effective action and anomalies in noncommutative theories
• Noncommutative QFT and Renormalization
• Heat-Kernel Approach to UV/IR Mixing on Isospectral Deformation Manifolds

Cited by in corpus (1)

• Loop Calculations for the Non-Commutative U(1) Gauge Field Model with Oscillator Term