arXiv subjects
Publications and source records attributed to Peter M. Lavrov.
We study systematically finite BRST-BFV transformations in $Sp(2)$-extended generalized Hamiltonian formalism. We present explicitly their Jacobians and the form of a solution to the compensation equation determining the functional field dependence of finite Fermionic parameters, necessary to generate arbitrary finite change of gauge-fixing functions in the path integral.
We study systematically finite BRST- BV transformations in the field-antifield formalism. We present explicitly their Jacobians and the form of a solution to the compensation equation determining the functional field dependence of finite Fermionic parameters, necessary to generate arbitrary finite change of gauge-fixing functions in the path integral.
In the framework of $Sp(2)$ extended Lagrangian field-antifield BV formalism we study systematically the role of finite field-dependent BRST-BV transformations. We have proved that the Jacobian of a finite BRST-BV transformation is capable of generating arbitrary finite change of the gauge-fixing function in the path integral.
Gribov and Zwanziger proposed a modification of Yang-Mills theory in order to cure the Gribov copy problem. We employ field-dependent BRST transformations to generalize the Gribov-Zwanziger model from the Landau gauge to general R_xi gauges. The Gribov horizon functional is presented in explicit form, in both the non-local and local variants. Finally, we show how to reach any given gauge from the Landau one.
We find an explicit form for the Jacobian of arbitrary field-dependent BRST transformations in Yang-Mills theory. For the functional-integral representation of the (gauge-fixed) Yang-Mills vacuum functional, such transformations merely amount to a precise change in the gauge-fixing functional. This proves the independence of the vacuum functional under any field-dependent BRST transformation. We also give a formula for the transformation parameter functional which generates a prescribed change of gauge and evaluate it for connecting two arbitrary R_xi gauges.
We explore the gauge dependence of the effective average action within the functional renormalization group (FRG) approach. It is shown that in the framework of standard definitions of FRG for the Yang-Mills theory, the effective average action remains gauge-dependent on-shell, independent on the use of truncation scheme. Furthermore, we propose a new formulation of the FRG, based on the use of composite operators. In this case one can provide on-shell gauge-invariance for the effective average action and universality of $S$-matrix.
Dependence of Green's functions for the Curci-Ferrari model on the parameter resembling the gauge parameter in massless Yang-Mills theories is investigated. It is shown that the generating functional of vertex functions (effective action) depends on this parameter on-shell.
The renormalization of general gauge theories on flat and curved space-time backgrounds is considered within the Sp(2)-covariant quantization method. We assume the existence of a gauge-invariant and diffeomorphism invariant regularization. Using the Sp(2)-covariant formalism one can show that the theory possesses gauge invariant and diffeomorphism invariant renormalizability to all orders in the loop expansion and the extended BRST symmetry after renormalization is preserved. The advantage of the Sp(2)-method compared to the standard Batalin-Vilkovisky approach is that, in reducible theories, the structure of ghosts and ghosts for ghosts and auxiliary fields is described in terms of irreducible representations of the Sp(2) group. This makes the presentation of solutions to the master equations in more simple and systematic way because they are Sp(2)- scalars.
We consider the renormalization of general gauge theories on curved space-time background, with the main assumption being the existence of a gauge-invariant and diffeomorphism invariant regularization. Using the Batalin-Vilkovisky (BV) formalism one can show that the theory possesses gauge invariant and diffeomorphism invariant renormalizability at quantum level, up to an arbitrary order of the loop expansion. Starting from this point we discuss the locality of the counterterms and the general prescription for constructing the power-counting renormalizable theories on curved background.