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Article
Report number	hep-lat/0210017 ; DPNU-02-32 ; CERN-TH-2002-254 ; CERN-TH-2002-254 ; DPNU-2002-32
Title	Lattice Perturbation Theory in Noncommutative Geometry and Parity Anomaly in 3D Noncommutative QED
Related title	QUANTUM ELECTRODYNAMICS
Author(s)	Nishimura, Jun (Nagoya U.) ; Vazquez-Mozo, Miguel A. (CERN)
Affiliation	(CERN)
Publication	2003
Imprint	11 Oct 2002
Number of pages	30
Note	Comments: 31 pages. LaTeX, feynmf. Minor changes, references added and typos corrected. Final version published in JHEP 31 pages. LaTeX, feynmf. Minor changes, references added and typos corrected. Final version published in JHEP
In:	JHEP 01 (2003) 075
DOI	10.1088/1126-6708/2003/01/075
Subject category	Particle Physics - Lattice
Abstract	We formulate lattice perturbation theory for gauge theories in noncommutative geometry. We apply it to three-dimensional noncommutative QED and calculate the effective action induced by Dirac fermions. In particular "parity invariance" of a massless theory receives an anomaly expressed by the noncommutative Chern-Simons action. The coefficient of the anomaly is labelled by an integer depending on the lattice action, which is a noncommutative counterpart of the phenomenon known in the commutative theory. The parity anomaly can also be obtained using Ginsparg-Wilson fermions, where the masslessness is guaranteed at finite lattice spacing. This suggests a natural definition of the lattice-regularized Chern-Simons theory on a noncommutative torus, which could enable nonperturbative studies of quantum Hall systems.

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