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Upadhyay, Sudhaker; Mandal, Bhabani Prasad

Noncommutative gauge theories: model for Hodge theory. (English) Zbl 1277.81082

Int. J. Mod. Phys. A 28, No. 25, Article ID 1350122, 15 p. (2013).
Summary: The nilpotent Becchi-Rouet-Stora-Tyutin (BRST), anti-BRST, dual-BRST and anti-dual-BRST symmetry transformations are constructed in the context of noncommutative (NC) 1-form as well as 2-form gauge theories. The corresponding Noether’s charges for these symmetries on the Moyal plane are shown to satisfy the same algebra, as by the de Rham cohomological operators of differential geometry. The Hodge decomposition theorem on compact manifold is also studied. We show that noncommutative gauge theories are field theoretic models for Hodge theory.

Cited in 4 Documents

MSC:

81T13 Yang-Mills and other gauge theories in quantum field theory
81T70 Quantization in field theory; cohomological methods
81R50 Quantum groups and related algebraic methods applied to problems in quantum theory
58A15 Exterior differential systems (Cartan theory)

Keywords:

noncommutative gauge theory; BRST symmetry; differential geometry
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