Field-dependent BRST Transformations Research Articles

Gribov horizon beyond the Landau gauge

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 Rξ 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.

Finite Nilpotent BRST Transformations in Hamiltonian Formulation

We consider the finite field dependent BRST (FFBRST) transformations in the context of Hamiltonian formulation using Batalin-Fradkin-Vilkovisky method. The non-trivial Jacobian of such transformations is calculated in extended phase space. The contribution from Jacobian can be written as exponential of some local functional of fields which can be added to the effective Hamiltonian of the system. Thus, FFBRST in Hamiltonian formulation with extended phase space also connects different effective theories. We establish this result with the help of two explicit examples. We also show that the FFBRST transformations is similar to the canonical transformations in the sector of Lagrange multiplier and its corresponding momenta.

Finite BRST transformation and constrained systems

We establish the connection between the generating functional for the first class theories and the generating functional for the second class theories using the finite field dependent BRST (FFBRST) transformation. We show this connection with the help of explicit calculations in two different models. The generating functional of the Proca model is obtained from the generating functional of the Stueckelberg theory for massive spin 1 vector field using FFBRST transformation. In the other example we relate the generating functionals for gauge invariant and gauge variant theories for a self-dual chiral boson.

Field dependent nilpotent symmetry for gauge theories

We construct the field dependent mixed BRST (combination of BRST and anti-BRST) transformations for pure gauge theories. These are shown to be an exact nilpotent symmetry of both the effective action as well as the generating functional for certain choices of the field dependent parameters. We show that the Jacobian contributions for path integral measure in the definition of generating functional arising from BRST and anti-BRST part compensate each other. The field dependent mixed BRST transformations are also considered in field/antifield formulation to show that the solutions of quantum master equation remain invariant under these. Our results are supported by several explicit examples.

Relating the generating functionals in field/antifield formulation through finite field dependent BRST transformation

We study the field/antifield formulation of pure Yang Mills theory in the framework of finite field dependent BRST transformation. We show that the generating functionals corresponding to different solutions of quantum master equation are connected through the finite field dependent BRST transformations. We establish this result with the help of several explicit examples.

Quantum gauge symmetry from finite field dependent BRST transformations

Using the technique of finite field dependent BRST transformations we show that the classical massive Yang–Mills theory and the pure Yang–Mills theory whose gauge symmetry is broken by a gauge fixing term are identical from the view point of quantum gauge symmetry. The explicit infinitesimal transformations which leave the massive Yang–Mills theory BRST invariant are given.