Abstract
The BFV formulation of a given gauge theory is usually significantly easier to obtain than its BV formulation. Based on foundational work by Fisch and Henneaux, Grigoriev and Damgaard introduced simple formulas for obtaining the latter from the former. Since BFV relies on the Hamiltonian version of the gauge theory, however, it does not come as a surprise that in general the resulting BV theory does not exhibit spacetime covariance. We provide an explicit example of this phenomenon in two spacetime dimensions and show how to restore covariance of the BV data by improving the Fisch-Henneaux-Grigoriev-Damgaard procedure with appropriate adaptations of their formulas.
Highlights
Quantum theory on the level of atoms and solid state physics uses Hamiltonian methods
The BFV formulation of a given gauge theory is usually significantly easier to obtain than its BV formulation
Since BFV relies on the Hamiltonian version of the gauge theory, it does not come as a surprise that in general the resulting BV theory does not exhibit spacetime covariance
Summary
Quantum theory on the level of atoms and solid state physics uses Hamiltonian methods. At least for the Poisson sigma model twisted by a WZ term, the implementation of the combination of the two field redefinitions — the one that brings ωB(FVHGD) into Darboux form (without changing the classical part of the BV action) followed by a BV symplectic transformation which leads to a covariant part of the BV action linear in the antifields — suffices to ensure covariance of all of the BV extension obtained in this way. As announced, this will lead to non-covariant formulas for both ωB(FVHGD) and SB(FVHGD).
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