Finite BRST-antiBRST Transformations in Lagrangian Formalism

We continue the study of finite BRST-antiBRST transformations for general gauge theories in Lagrangian formalism initiated in [arXiv:1405.0790[hep-th]], with a doublet $λ_{a}$, $a=1,2$, of anticommuting Grassmann parameters, and find an explicit Jacobian corresponding to this change of variables for constant $λ_{a}$. This makes it possible to derive the Ward identities and their consequences for the generating functional of Green's functions. We announce the form of the Jacobian [proved to be correct in [arXiv:1406.5086[hep-th]] for finite field-dependent BRST-antiBRST transformations with functionally-dependent parameters, $λ_{a}$, induced by a finite even-valued functional $Λ(ϕ,π,λ)$ and by the generators $s_{a}$ of BRST-antiBRST transformations acting in the space of fields $ϕ$, antifields $ϕ_{a}^{\ast}$, $\bar ϕ$ and auxiliary variables $π^{a},λ$. On the basis of this Jacobian, we solve a compensation equation for $Λ$, which is used to achieve a precise change of the gauge-fixing functional for an arbitrary gauge theory. We derive a new form of the Ward identities containing the parameters $λ_{a}$ and study the problem of gauge-dependence. The general approach is exemplified by the Freedman--Townsend model of\ a non-Abelian antisymmetric tensor field.

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