Noncommutative U(1) gauge theory from a worldline perspective

Abstract

We study pure noncommutative U(1) gauge theory representing its one-loop effective action in terms of a phase space worldline path integral. We write the quadratic action using the background field method to keep explicit gauge invariance, and then employ the worldline formalism to write the one-loop effective action, singling out UV-divergent parts and finite (planar and non-planar) parts, and study renormalization properties of the theory. This amounts to employ worldline Feynman rules for the phase space path integral, that nicely incorporate the Fadeev-Popov ghost contribution and efficiently separate planar and non-planar contributions. We also show that the effective action calculation is independent of the choice of the worldline Green's function, that corresponds to a particular way of factoring out a particle zero-mode. This allows to employ homogeneous string-inspired Feynman rules that greatly simplify the computation.

arXiv comment27+1 pages. Minor corrections; matches published version

References in corpus (21)

• Noncommutative Field Theory
• Quantum Field Theory on Noncommutative Spaces
• Noncommutative Perturbative Dynamics
• Perturbative Quantum Field Theory in the String-Inspired Formalism
• A Gravity Theory on Noncommutative Spaces
• The IR/UV Connection in the Non-Commutative Gauge Theories
• Renormalisation of ϕ^4-theory on noncommutative R^4 in the matrix base
• An Introduction to Noncommutative Spaces and their Geometry
• The One-loop UV Divergent Structure of U(1) Yang-Mills Theory on Noncommutative R^4
• Gravity in Non-Commutative Geometry
• Duality in Scalar Field Theory on Noncommutative Phase Spaces
• Perturbative analysis on infrared and ultraviolet aspects of noncommutative QED on R^4
• Vanishing of Beta Function of Non Commutative ${\Phi }_4^4$ Theory to all orders
• Perturbative quantum gauge fields on the noncommutative torus
• Noncommutative Induced Gauge Theory
• Gauge-fixing independence of IR divergences in non-commutative U(1), perturbative tachyonic instabilities and supersymmetry
• One Loop Renormalizability of Supersymmetric Yang-Mills Theories on Noncommutative Two-Torus
• Induced Gauge Theory on a Noncommutative Space
• Non-Commutative U(1) Gauge Theory on R**4 with Oscillator Term and BRST Symmetry
• BRST treatment of zero modes for the worldline formalism in curved space
• Heat kernel, effective action and anomalies in noncommutative theories

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• $U(N)$ Yang-Mills in non-commutative space time
• Non-commutativity in polar coordinates
• Nonlocal Lagrangian fields and the second Noether theorem. Non-commutative $U(1)$ gauge theory
• Induced Action for Conformal Higher Spins from Worldline Path Integrals
• $\mathcal{O}(\theta )$ Feynman rules for quadrilinear gauge boson couplings in noncommutative standard model