On Non-Commutative U*(1) Gauge Models and Renormalizability

Abstract

Based on our recent findings regarding (non-)renormalizability of non-commutative U*(1) gauge theories [arxiv:0908.0467, arxiv:0908.1743] we present the construction of a new type of model. By introducing a soft breaking term in such a way that only the bilinear part of the action is modified, no interaction between the gauge sector and auxiliary fields occurs. Demanding in addition that the latter form BRST doublet structures, this leads to a minimally altered non-commutative U*(1) gauge model featuring an IR damping behavior. Moreover, the new breaking term is shown to provide the necessary structure in order to absorb the inevitable quadratic IR divergences appearing at one-loop level in theories of this kind. In the present paper we compute Feynman rules, symmetries and results for the vacuum polarization together with the one-loop renormalization of the gauge boson propagator and the three-point functions.

20 pages, 4 figures; v2-v4: clarified several points, and minor corrections

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• Involutive representations of coordinate algebras and quantum spaces
• Gauge fields on noncommutative geometries with curvature
• BPHZ renormalization and its application to non-commutative field theory
• Aspects of perturbative quantum field theory on non-commutative spaces
• The Gribov problem in Noncommutative gauge theory
• Photon polarization tensor on deformed spacetime: A four-photon-tadpole contribution
• One-loop structure of the U(1) gauge model on the truncated Heisenberg space
• Spectral theorem in noncommutative field theories: Jacobi dynamics
• Gauge Fields on Non-Commutative Spaces and Renormalization
• Extended BRST formulation of a non-commutative U(1) gauge model
• On NCQFT and dimensionless insertions