The physical state condition in the BRST quantization of Chern-Simons field theory is used to derive Gauss law constraints in the presence of Wilson loops, which play important role in explicitly establishing the connection of Chern-Simons field theory with 2-dimensional conformal field theory. When we discuss knot invariants in terms of Chern-Simons theory [1–6] and the relationship between Ch...

We introduce a geometric framework needed for a mathematical understanding of the BRST symmetries and chiral anomalies in gauge field theories. We define the BRST bicomplex in terms of local cohomology using differential forms on the infinite jet bundle and consider variational aspects of the problem in this cohomological context. The adjoint representation of the structure group induces a repr...

Hamiltonian BRST formalism (FV formalism) includes many auxiliary fields without explanation. Its path-integration has a simple form by using BRST charge, but its construction is quite mechanically and hard to understand physical meaning. In this paper we perform the phase space path-integral with requiring BRST invariance for action and measure, and show that the resultant form is equivalent t...

We investigate the infrared limit of the quantum equation of motion of the gauge boson propagator in various gauges and models with a BRST symmetry. We find that the saturation of this equation at low momenta distinguishes between the Coulomb, Higgs and confining phase of the gauge theory. The Coulomb phase is characterized by a massless gauge boson. Physical states contribute to the saturation...

We study the topological mass generation in the 4 dimensional nonabelian gauge theory, which is the extension of the Allen et al.’s work in the abelian theory. It is crucial to introduce a one form auxiliary field in constructing the gauge invariant nonabelian action which contains both the one form vector gauge field A and the two form antisymmetric tensor field B. As in the abelian case, the ...

We demonstrate that the nilpotent Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry invariance of the Lagrangian density of a four (3 + 1)-dimensional (4D) non-Abelian 1-form gauge theory with Dirac fields can be captured within the framework of the superfield approach to BRST formalism. The above 4D theory, where there is an explicit coupling between the non-Abelian 1-form gauge field an...

We exploit the geometrical superfield formalism to derive the local, covariant and continuous Becchi-Rouet-Stora-Tyutin (BRST) symmetry transformations and the non-local, non-covariant and continuous dual-BRST symmetry transformations for the free Abelian one-form gauge theory in four (3+1)-dimensions (4D) of spacetime. Our discussion is carried out in the framework of BRST invariant Lagrangian...

We discuss the (dual-)gauge transformations and BRST cohomology for the two (1 + 1)-dimensional (2D) free Abelian one-form and four (3 + 1)-dimensional (4D) free Abelian 2-form gauge theories by exploiting the (co-)BRST symmetries (and their corresponding generators) for the Lagrangian densities of these theories. For the 4D free 2-form gauge theory, we show that the changes on the antisymmetri...

Closed string physical states are BRST cohomology classes computed on the space of states annihilated by b−0 . Since b − 0 does not commute with the operations of picture changing, BRST cohomologies at different pictures need not agree. We show explicitly that RamondRamond (RR) zero-momentum physical states are inequivalent at different pictures, and prove that non-zero momentum physical states...

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 tak...