Hamiltonian BRST Formalisms Research Articles

Hamiltonian BRST-invariant deformations in Abelian gauge theory with higher derivative matter fields

We construct the consistent interactions among the Abelian gauge fields and various higher derivative matter fields within the framework of the Hamiltonian BRST formalism. To achieve this, we mainly investigate a set of iterative equations with respect to the free model under study by using the cohomological technique. Concretely, it is shown that the second-order and the other higher-order deformations of the BRST charge are supposed to be zero. While for the BRST-invariant Hamiltonian, the third-order as well as the corresponding higher-order deformation terms vanish completely for scalar fields. In special, the deformation of BRST-invariant Hamiltonian for the spinor field model terminates at order one as we can imagine. Furthermore, after plugging these deformed quantities into the original Hamiltonian and exploiting the ghost-independent terms, we recover the usual local gauge symmetries of the resulting interacting theory which can be interpreted as the gaugings of the rigid invariance of the uncoupled system.

Remark on the classical solution of the Chaplygin gas as d-branes

The classical solution of bosonic d-brane in (d+1,1) space-time is studied. We work with light-cone gauge and reduce the problem into Chaplygin gas problem. The static equation is equivalent to vanishing of extrinsic mean curvature, which is similar to Einstein equation in vacuum. We show that the d-brane problem in this gauge is closely related to Plateau problem, and we give some non-trivial solutions from minimal surfaces. The solutions of d-1,d,d+1 spatial dimensions are obtained from d-dimensional minimal surfaces as solutions of Plateau problem. In addition we discuss on the relation to Hamiltonian-BRST formalism for d-branes.

BRST FORMALISM FOR SYSTEMS WITH HIGHER ORDER DERIVATIVES OF GAUGE PARAMETERS

For a wide class of mechanical systems, invariant under gauge transformations with arbitrary higher order time derivatives of gauge parameters, the equivalence of Lagrangian and Hamiltonian BRST formalisms is proved. It is shown that the Ostrogradsky formalism establishes the natural rules to relate the BFV ghost canonical pairs with the ghosts and antighosts introduced by the Lagrangian approach. Explicit relation between corresponding gauge-fixing terms is obtained.

The Hamiltonian BRST quantization of massive abelianp-form gauge fields

In this paper we quantize the massive abelian p-form gauge fields in D dimensions in the context of the Hamiltonian BRST formalism. Extending the original phase-space in order to reveal the reducibility of a certain first-class system, we obtain that quantizing the original theory is the same as quantizing a (p - 1)-order reducible system using BRST. This system describes abelian p-form gauge fields interacting through a current - current term with abelian (p - 1)-form gauge fields. For p = 1 and D = 4 we recover the Stueckelberg coupling.

Equivalence between Lagrangian and Hamiltonian BRST formalisms

For a wide class of gauge invariant systems, the equivalence between Lagrangian and Hamiltonian BRST formalisms is proven.

Hamiltonian brst formalism for gauge-invariant systems with closed algebra

The systems for which the algebra of gauge transformations in the lagrangian formalism is closed, are considered. The hamiltonian BRST charge and the BRST-invariant hamiltonian are found explicitly. Their expansions in powers of the ghost variables contain, in general, an infinite number of terms.

Non-abelian chiral bosons coupled to gauge field

By imposing constraints on the phase space of the bosonic description of N Dirac fermions, chirally coupled to a U( N) gauge field in two dimensions, we construct a natural coupling of non-abelian chiral bosons to a gauge field. Analysing the constraints structure of the theory we show that non-abelian chiral bosons coupled to a gauge field may be viewed as a gauge fixed version of a gauge invariant theory. Using the hamiltonian BRST formalism we quantize the theory and derive a unitarity restriction.

Lagrangian and Hamiltonian BRST formalisms

We establish, at the classical level, the equivalence between the standard BRST hamiltonian formalism and the lagranian BRST approach with fields and antifields for irreducible first rank theories.