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We study the construction of the classical nilpotent canonical BRST charge for the nonlinear gauge algebras where a commutator (in terms of Poisson brackets) of the constraints is a finite order polynomial of the constraints.
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We study the construction of the classical nilpotent canonical BRST charge for the nonlinear gauge algebras where a commutator (in terms of Poisson brackets) of the constraints is a finite order polynomial of the constraints. Such a polynomial is characterized by the coefficients forming a set of higher order structure constraints. Assuming the set of constraints to be linearly independent, we find the restrictions on the structure constraints when the nilpotent BRST charge can be written in a simple and universal form. In the case of quadratically nonlinear algebras we find the expression for third order contribution in the ghost fields to the BRST charge without the use of any additional restrictions on the structure constants.
We give the explicite form of the BRST charge Q for the algebra W_4=WA_3 in the basis where the spin-3 and the spin-4 field are primary as well as for a basis where the algebra closes quadratically.
A general method of the BRST--anti-BRST symmetric conversion of second-class constraints is presented. It yields a pair of commuting and nilpotent BRST-type charges that can be naturally regarded as BRST and anti-BRST ones. Interchanging the BRST and anti-BRST generators corresponds to a symmetry between the original second-class constraints and the conversion variables, which enter the formalism on equal footing.
A complete analysis of the canonical structure for a gauge fixed PST bosonic five brane action is performed. This canonical formulation is quadratic in the dependence on the antisymmetric field and it has second class constraints. We remove the second class constraints and a master canonical action with only first class constraints is proposed. The nilpotent BRST charge and its BRST invariant effective theory is constructed. The construction does not assume the existence of the inverse of the induced metric. Singular configurations are then physical ones. We obtain the physical Hamiltonian of the theory and analyze its stability properties. Finally, by studying the algebra of diffeomorphisms we find under mild assumptions the general structure for the Hamiltonian constraint for theories invariant under 6 dimensional diffeomorphisms and we give an algebraic characterization of the constraint associated with the bosonic five brane action. We also identify the constraint for the bosonic five brane action upgraded with a cosmological term, it contains a Born-Infeld type term.
We present the BRST cohomologies of a class of constraint (super) Lie algebras as detour complexes. By giving physical interpretations to the components of detour complexes as gauge invariances, Bianchi identities and equations of motion we obtain a large class of new gauge theories. The pivotal new machinery is a treatment of the ghost Hilbert space designed to manifest the detour structure. Along with general results, we give details for three of these theories which correspond to gauge invariant spinning particle models of totally symmetric, antisymmetric and Kahler antisymmetric forms. In particular, we give details of our recent announcement of a (p,q)-form Kahler electromagnetism. We also discuss how our results generalize to other special geometries.
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