Induced Gauge Theory on a Noncommutative Space

Abstract

We consider a scalar ${\varphi }^4$ theory on canonically deformed Euclidean space in 4 dimensions with an additional oscillator potential. This model is known to be renormalisable. An exterior gauge field is coupled in a gauge invariant manner to the scalar field. We extract the dynamics for the gauge field from the divergent terms of the 1-loop effective action using a matrix basis and propose an action for the noncommutative gauge theory, which is a candidate for a renormalisable model.

Typos corrected, one reference added; eqn. (49) corrected, one equation number added; 30 pages

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Cited by in corpus (65)

• Emergent Gravity from Noncommutative Gauge Theory
• Vacuum configurations for renormalizable non-commutative scalar models
• On the Problem of Renormalizability in Non-Commutative Gauge Field Models - A Critical Review
• Combinatorial Dyson-Schwinger equations in noncommutative field theory
• Emergent Gravity, Matrix Models and UV/IR Mixing
• Translation-invariant models for non-commutative gauge fields
• On the vacuum states for noncommutative gauge theory
• One-Loop Calculations for a Translation Invariant Non-Commutative Gauge Model
• Noncommutative field theories on $R_{\lambda }^3$: Towards UV/IR mixing freedom
• Non-Commutative U(1) Gauge Theory on R**4 with Oscillator Term and BRST Symmetry
• 8D-spectral triple on 4D-Moyal space and the vacuum of noncommutative gauge theory
• Commutative limit of a renormalizable noncommutative model
• Noncommutative epsilon-graded connections
• The absence of the 4$\psi$ divergence in noncommutative chiral models
• Quantum gauge theories on noncommutative 3-d space
• Parametric representation of a translation-invariant renormalizable noncommutative model
• Noncommutative geometry, gauge theory and renormalization
• $\kappa$-Poincaré invariant quantum field theories with KMS weight
• Loop Calculations for the Non-Commutative U(1) Gauge Field Model with Oscillator Term
• Noncommutative gauge theories on ${\mathbb{R}}_{\theta }^2$ as matrix models
• Gauge theories on $\kappa$-Minkowski spaces: Twist and modular operators
• Spectral geometry of the Moyal plane with harmonic propagation
• Deformation Quantization for Heisenberg Supergroup
• Exact Partition Functions for Gauge Theories on ${\mathbb{R}}_{\lambda }^3$
• On Non-Commutative U*(1) Gauge Models and Renormalizability
• Noncommutative gauge theories on ${\mathbb{R}}_{\lambda }^3$: Perturbatively finite models
• Noncommutative Induced Gauge Theories on Moyal Spaces
• Connes distance by examples: Homothetic spectral metric spaces
• Slavnov-Taylor identities, non-commutative gauge theories and infrared divergences
• Closed star product on noncommutative ${\mathbb{R}}^3$ and scalar field dynamics
• A New Approach to Non-Commutative U(N) Gauge Fields
• Symmetries of noncommutative scalar field theory
• Remarks on the 2nd order Seiberg-Witten maps
• Renormalizability and Phenomenology of theta-expanded Noncommutative Gauge Field Theory
• Noncommutative U(1) gauge theory from a worldline perspective
• Heat Trace Asymptotics on Noncommutative Spaces
• One-loop $\beta$ functions of a translation-invariant renormalizable noncommutative scalar model
• Involutive representations of coordinate algebras and quantum spaces
• Twisted BRST symmetry in gauge theories on $\kappa$-Minkowski
• On the Origin of the Harmonic Term in Noncommutative Quantum Field Theory
• Gauge fields on noncommutative geometries with curvature
• Derivations of the Moyal Algebra and Noncommutative Gauge Theories
• Examples of derivation-based differential calculi related to noncommutative gauge theories
• BPHZ renormalization and its application to non-commutative field theory
• On the Renormalization of Non-Commutative Field Theories
• Heat kernel expansion and induced action for the matrix model Dirac operator
• Quantum instability of gauge theories on $\kappa$-Minkowski space
• Aspects of perturbative quantum field theory on non-commutative spaces
• One-loop structure of the U(1) gauge model on the truncated Heisenberg space
• Translation-Invariant Noncommutative Renormalization
• One loop radiative corrections to the translation-invariant noncommutative Yukawa Theory
• Strong Field, Noncommutative QED
• $U(N)$ Yang-Mills in non-commutative space time
• Quantization of a gauge theory on a curved noncommutative space
• Spectral theorem in noncommutative field theories: Jacobi dynamics
• Renormalization of the commutative scalar theory with harmonic term to all orders
• Spinors on a curved noncommutative space: coupling to torsion and the Gross-Neveu model
• On Batalin-Vilkovisky Formalism of Non-Commutative Field Theories
• Noncommutative Supergeometry and Quantum Supergroups
• Induced Gauge Theory on a Noncommutative Space
• Gauge Fields on Non-Commutative Spaces and Renormalization
• A numerical approach to harmonic non-commutative spectral field theory
• Extended BRST formulation of a non-commutative U(1) gauge model
• Noncommutative field theories with harmonic term
• Algebraic structures in $\kappa$-Poincaré invariant gauge theories