The regularization scheme is proposed for the constrained Hamil-tonian formulation of the gauge fields coupled to the chiral or axial fermions. The Schwinger terms in the regularized operator first-class constraint algebra are shown to be consistent with the covariant divergence anomaly of the corresponding current. Regularized quantum master equations are studied, and the Schwinger terms are f...

We discuss the algebraic structure of the various BRST symmetries associated with topological Yang-Mills theory as a generalization of the BRS analysis developed for the non-Abelian anomaly in the local Yang-Mills theory. We show that our BRST algebra leads to an extended Russian formula and descent equations, which contains the descent equation of Yang-Mills theory as sub-relations. We propose...

We discuss some of the topological features of a non-interacting two (1 + 1)-dimensional Abelian gauge theory in the framework of superfield formulation. This theory is described by a BRST invariant Lagrangian density in the Feynman gauge. We express the local and continuous symmetries, Lagrangian density, topological invariants and symmetric energy momentum tensor of the theory in the language...

Conditions which must be satisfied by the gauge-fixing fermion χ used in the BRST quantisation of constrained systems are established. These ensure that the extension of the Hamiltonian by the gaugefixing term [Ω, χ] (where Ω is the BRST charge) gives the correct path integral. In canonical BRST quantisation (particularly the path-integral approach developed by Batalin, Fradkin, Fradkina and Vi...

We argue that the BRST and the anti-BRST super symmetries in the four-dimensional Yang-Mills theory can be spontaneously broken in a nonlinear partial gauge due to ghost–anti-ghost condensation. However, we show that the spontaneous BRST symmetry breaking can be avoided if we adopt the modified Maximal Abelian gauge which is an orthosymplectic OSp(4|2) invariant renormalizable gauge proposed by...

We determine the nilpotent BRST and anti-BRST transformations for the Cho–Faddeev-Niemi variables for the SU(2) Yang-Mills theory based on the new interpretation given in the previous paper of the Cho–Faddeev-Niemi decomposition. This gives a firm ground for performing the BRST quantization of the Yang–Mills theory written in terms of the Cho–Faddeev-Niemi variables. We propose also a modified ...

We discuss in detail the relation between the gauge fixed and gauge invariant BRST cohomology. We showed previously that in certain gauges some cohomology classes of the gauge-fixed BRST differential do not correspond to gauge invariant observables. We now show that in addition “accidental” conserved currents may appear. These correspond one-toone to observables that become trivial in this gaug...

A generalization of BRST field theory is presented, based on wave operators for the fields constructed out of, but different from the BRST operator. We discuss their quantization, gauge fixing and the derivation of propagators. We show, that the generalized theories are relevant to relativistic particle theories in the Brink-Di Vecchia-Howe-Polyakov (BDHP) formulation, and argue that the same p...

Conditions which must be satisfied by the gauge-fixing fermion χ used in the BRST quantisation of constrained systems are established. These ensure that the extension of the Hamiltonian by the gaugefixing term [Ω, χ] (where Ω is the BRST charge) gives the correct path integral. In canonical BRST quantisation (particularly the path-integral approach developed by Batalin, Fradkin, Fradkina and Vi...

We present the massless six-point one-loop amplitudes in the open and closed superstring using BRST cohomology arguments from the pure spinor formalism. The hexagon gauge anomaly is traced back to a class of kinematic factors in pure spinor superspace which were recently introduced as BRST pseudo-invariants. This complements previous work where BRST invariance arguments were used to derive the ...