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.

27+1 pages. Minor corrections; matches published version

References in corpus (5)

• A Gravity Theory on Noncommutative Spaces
• Vanishing of Beta Function of Non Commutative ${\Phi }_4^4$ Theory to all orders
• Noncommutative Induced Gauge Theory
• Induced Gauge Theory on a Noncommutative Space
• Non-Commutative U(1) Gauge Theory on R**4 with Oscillator Term and BRST Symmetry

Cited by in corpus (10)

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• Spinning Particles in Quantum Mechanics and Quantum Field Theory
• $U(N)$ 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