Cohomological aspects of Abelian gauge theory

Details Cohomological aspects of Abelian gauge theory Cohomological aspects of Abelian gauge theory

1999-02-22

arxiv.org/abs/hep-th/9902146v3

J. Phys. A: Math Gen 33 (2000) 2437-2446

Physics

High Energy Physics

High Energy Physics - Theory

12 pages, LaTeX, no figures, Title and text have been slightly changed, Journal reference is given and a reference has been ad

Scientific paper

10.1088/0305-4470/33/12/310

We discuss some aspects of cohomological properties of a two-dimensional free Abelian gauge theory in the framework of BRST formalism. We derive the conserved and nilpotent BRST- and co-BRST charges and express the Hodge decomposition theorem in terms of these charges and a conserved bosonic charge corresponding to the Laplacian operator. It is because of the topological nature of free U(1) gauge theory that the Laplacian operator goes to zero when equations of motion are exploited. We derive two sets of topological invariants which are related to each-other by a certain kind of duality transformation and express the Lagrangian density of this theory as the sum of terms that are BRST- and co-BRST invariants. Mathematically, this theory captures together some of the key features of Witten- and Schwarz type of topological field theories.

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