On the Renormalizability of Noncommutative U(1) Gauge Theory - an Algebraic Approach

Abstract

We investigate the quantum effects of the nonlocal gauge invariant operator $\frac{1}{D^2}{F}_{\mu \nu }\ast \frac{1}{D^2}{F}^{\mu \nu }$ in the noncommutative U(1) action and its consequences to the infrared sector of the theory. Nonlocal operators of such kind were proposed to solve the infrared problem of the noncommutative gauge theories evading the questions on the explicit breaking of the Lorentz invariance. More recently, a first step in the localization of this operator was accomplished by means of the introduction of an extra tensorial matter field, and the first loop analysis was carried out $(Eur.Phys.J.\text{C62}:433-443,2009)$. We will complete this localization avoiding the introduction of new degrees of freedom beyond those of the original action by using only BRST doublets. This will allow us to make a complete BRST algebraic study of the renormalizability of the theory, following Zwanziger's method of localization of nonlocal operators in QFT.

standard Latex no figures, version2 accepted in J. Phys A: Math Theor

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Cited by in corpus (15)

• Quantum gauge theories on noncommutative 3-d space
• Gauge theories on quantum spaces
• Loop Calculations for the Non-Commutative U(1) Gauge Field Model with Oscillator Term
• On Non-Commutative U*(1) Gauge Models and Renormalizability
• Gauge Theories on Deformed Spaces
• A New Approach to Non-Commutative U(N) Gauge Fields
• Consistent Anomalies in Translation-Invariant Noncommutative Gauge Theories
• On UV/IR Mixing via Seiberg-Witten Map for Noncommutative QED
• One-Loop Calculations and Detailed Analysis of the Localized Non-Commutative 1/p**2 U(1) Gauge Model
• Gribov as a Phase Transition
• Translation-Invariant Noncommutative Renormalization
• One loop radiative corrections to the translation-invariant noncommutative Yukawa Theory
• Gauge Fields on Non-Commutative Spaces and Renormalization
• Extended BRST formulation of a non-commutative U(1) gauge model
• On NCQFT and dimensionless insertions