Quantum BRST operators in the extended BRST-anti-BRST formalism

The quantum BRST-anti-BRST operators are explicitely derived and the consequences related to correlation functions are investigated. The connection with the standard formalism and the loopwise expansions for quantum operators and anomalies in Sp(2) approach are analyzed.Comment: 7 page

Spacetime locality in Sp(2) symmetric lagrangian formalism

The existence of a local solution to the Sp(2) master equation for gauge field theory is proven in the framework of perturbation theory and under standard assumptions on regularity of the action. The arbitrariness of solutions to the Sp(2) master equation is described, provided that they are proper. It is also shown that the effective action can be chosen to be Sp(2) and Lorentz invariant (under the additional assumption that the gauge transformation generators are Lorentz tensors).Comment: LaTeX, 13 pages, minor misprints correcte

On the multilevel generalization of the field--antifield formalism

The multilevel geometrically--covariant generalization of the field--antifield BV--formalism is suggested. The structure of quantum generating equations and hypergauge conditions is studied in details. The multilevel formalism is established to be physically--equivalent to the standard BV--version.Comment: 10 pages, FIAN/TD/13--9

On possible generalizations of field--antifield formalism

A generalized version is proposed for the field-antifield formalism. The antibracket operation is defined in arbitrary field-antifield coordinates. The antisymplectic definitions are given for first- and second-class constraints. In the case of second-class constraints the Dirac's antibracket operation is defined. The quantum master equation as well as the hypergauge fixing procedure are formulated in a coordinate-invariant way. The general hypergauge functions are shown to be antisymplectic first-class constraints whose Jacobian matrix determinant is constant on the constraint surface. The BRST-type generalized transformations are defined and the functional integral is shown to be independent of the hypergauge variations admitted. In the case of reduced phase space the Dirac's antibrackets are used instead of the ordinary ones

On the Perturbative Equivalence Between the Hamiltonian and Lagrangian Quantizations

The Hamiltonian (BFV) and Lagrangian (BV) quantization schemes are proved to be equivalent perturbatively to each other. It is shown in particular that the quantum master equation being treated perturbatively possesses a local formal solution.Comment: 14 pages, LaTeX, no figure

On the equivalence between the unified and standard versions of constraint dynamics

The structure of physical operators and states of the unified constraint dynamics is studied. The genuine second--class constraints encoded are shown to be the superselection operators. The unified constrained dynamics is established to be physically--equivalent to the standard BFV--formalism with constraints split.Comment: 10 pages, FIAN/TD/12--9

On the Multilevel Field--Antifield Formalism with the Most General Lagrangian Hypergauges

The multilevel field-antifield formalism is constructed in a geometrically covariant way without imposing the unimodularity conditions on the hypergauge functions. Thus the previously given version [1,2] is extended to cover the most general case of Lagrangian surface bases. It is shown that the extra measure factors, required to enter the gauge-independent functional integrals, can be included naturally into the multilevel scheme by modifying the boundary conditions to the quantum master equation.Comment: 9, P.N.Lebedev Physical Institute, I.E.Tamm Theory Departmen

"Planck-scale physics" of vacuum in a strong magnetic field

It is widely believed that Lorentz symmetry of physical vacuum is broken near the Planck scale. Here we show that recently demonstrated "hyperbolic metamaterial" behaviour of vacuum in a strong magnetic field provides us with an interesting analogy of the Planck-scale physics. As demonstrated by Chernodub, strong magnetic field forces vacuum to develop real condensates of electrically charged \rho mesons, which form an anisotropic inhomogeneous superconducting state similar to Abrikosov vortex lattice. As far as electromagnetic field behaviour is concerned, this hyperbolic metamaterial state of vacuum exhibits effective 3D Lorentz symmetry, which is broken at small scale (large momenta) due to spatial dispersion. Thus, an effective Lorentz symmetry-violating "Planck scale" may be introduced. Near the critical magnetic field this effective "Planck scale" is much larger than the metamaterial periodicity defined by the \rho meson lattice. Similar to regular hyperbolic metamaterials, spatial dispersion of vacuum in a strong magnetic field leads to appearance of the "additional wave", which manifests itself as a "heavy" extraordinary photon with an effective mass ~2GeV.Comment: 14 pages, 2 figures, this version is accepted for publication in Phys.Rev.

Degenerate Odd Poisson Bracket on Grassmann Variables

A linear degenerate odd Poisson bracket (antibracket) realized solely on Grassmann variables is presented. It is revealed that this bracket has at once three nilpotent $\Delta$-like differential operators of the first, the second and the third orders with respect to the Grassmann derivatives. It is shown that these $\Delta$-like operators together with the Grassmann-odd nilpotent Casimir function of this bracket form a finite-dimensional Lie superalgebra.Comment: 5 pages, LATEX. Corrections of misprints. The relation (23) is adde