On the Brst Cohomology in U(1) Gauge Theory

We discuss the Becchi-Rouet-Stora-Tyutin (BRST) cohomology in the case of twodimensional free U(1) gauge theory. In addition to the usual BRST charge, we deduce a conserved and nilpotent dual-BRST charge under which the gauge-fixing term remains invariant. This charge is the analogue of the adjoint(dual) exterior derivative of differential geometry. The BRST extended Casimir operator, corresponding to the Laplacian operator of differential geometry, turns out to generate a symmetry under which the ghost term remains invariant. We take a single photon state in the Hilbert space and demonstrate the notion of gauge invariance, no-(anti)ghost theorem and transversality of photon by exploiting the refinement of cohomology by selecting the physical state as the harmonic state of the Hodge decomposition theorem. On leave of absence from Bogoliubov Laboratory of Theoretical Physics, JINR-Dubna, Moscow, Russia. e-mail addresses: [email protected] AND [email protected]