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 ${\lambda }_a$, $a=1,2$, of anticommuting Grassmann parameters, and find an explicit Jacobian corresponding to this change of variables for constant ${\lambda }_a$. 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, $\lambda_{a}% =s_{a}\Lambda$,inducedbyafiniteeven-valuedfunctional$\Lambda(\phi ,\pi,\lambda)$andbythegenerators$s_{a}$ of BRST-antiBRST transformations acting in the space of fields $\varphi$, antifields ${\varphi }_a^{\ast }$, $\bar {\phi}$andauxiliaryvariables$\pi^{a},\lambda$. On the basis of this Jacobian, we solve a compensation equation for $\mathrm{\Lambda }$, 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 ${\lambda }_a$ and study the problem of gauge-dependence. The general approach is exemplified by the Freedman–Townsend model of\ a non-Abelian antisymmetric tensor field.