Comments on the covariant Sp(2)-symmetric Lagrangian BRST formalism

Abstract

We give a simple geometrical picture of the basic structures of the covariant Sp(2) symmetric quantization formalism -triplectic quantization -recently suggested by Batalin, Marnelius and Semikhatov. In particular, we show that the appearance of an even Poisson bracket is not a particular property of triplectic quantization. Rather, any solution of the classical master equation generates on a Lagrangian surface of the antibracket an even Poisson bracket. Also other features of triplectic quantization can be identified with aspects of conventional Lagrangian BRST quantization without extended BRST symmetry. * On leave of absence from the

Superfield BRST charge and the master action

“…[12,13,14]). It would also be interesting to consider the isomorphism between the Poisson bracket and the antibracket [15] in the light of this superfield construction.…”

Non-Abelian antibrackets

“…It should also be interesting to investigate the Poisson brackets and Nambu brackets generated by the generalized antibrackets and suitable vector fields V anticommuting with the generalized ∆-operator (and in particular certain Hamiltonian vector fields within the antibrackets), as described in the case of the usual antibracket in ref. [20].…”

Effective action of composite fields for general gauge theories in Batalin, Lavrov, and Tyutin covariant formalism

“…The various aspects and properties of the gauge field theory within the BV quantization have been under study for quite a long time by now and may be considered as well-known ones (see, for example, reviews [3,4]). On the same time the study of properties as well as various possibilities of interpretation and generalizations of gauge theories in the BLT quantization [2] has been started quite recently [5][6][7][8][9][10][11][12][13][14][15][16]. Following the line of the research of refs.…”

“…Following the line of the research of refs. [5][6][7][8][9][10][11][12][13][14][15][16] present paper is devoted to the study of one of the central problems arising in quantum gauge field theory within the Lagrangian formalism, i.e. gauge dependence of generating functionals of Green's functions in general gauge theories with composite fields.…”