BRST cohomology and Hodge decomposition theorem in Abelian gauge theory

Details BRST cohomology and Hodge decomposition theorem in Abelian gauge theory BRST cohomology and Hodge decomposition theorem in Abelian gauge theory

1998-08-07

arxiv.org/abs/hep-th/9808040v2

Int. J. Mod. Phys. A15 (2000) 1685-1705

Physics

High Energy Physics

High Energy Physics - Theory

20 pages, LaTeX, no figures, Title and text have been changed, Journal reference is given, some references have been added

Scientific paper

10.1142/S0217751X00000756

We discuss the Becchi-Rouet-Stora-Tyutin (BRST) cohomology and Hodge decomposition theorem for the two dimensional free U(1) gauge theory. In addition to the usual BRST charge, we derive a local, conserved and nilpotent co(dual)-BRST charge under which the gauge-fixing term remains invariant. We express the Hodge decomposition theorem in terms of these charges and the Laplacian operator. We take a single photon state in the quantum Hilbert space and demonstrate the notion of gauge invariance, no-(anti)ghost theorem, transversality of photon and establish the topological nature of this theory by exploiting the concepts of BRST cohomology and Hodge decomposition theorem. In fact, the topological nature of this theory is encoded in the vanishing of the Laplacian operator when equations of motion are exploited. On the two dimensional compact manifold, we derive two sets of topological invariants with respect to the conserved and nilpotent BRST- and co-BRST charges and express the Lagrangian density of the theory as the sum of terms that are BRST- and co-BRST invariants. Mathematically, this theory captures together some of the key features of both Witten- and Schwarz type of topological field theories.

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