Antisymplectic Gauge Theories

A general field-antifield BV formalism for antisymplectic first class constraints is proposed. It is as general as the corresponding symplectic BFV-BRST formulation and it is demonstrated to be consistent with a previously proposed formalism for antisymplectic second class constraints through a generalized conversion to corresponding first class constraints. Thereby the basic concept of gauge symmetry is extended to apply to quite a new class of gauge theories potentially possible to exist.Comment: 13 pages,Latexfile,New introductio

Reducible Gauge Algebra of BRST-Invariant Constraints

We show that it is possible to formulate the most general first-class gauge algebra of the operator formalism by only using BRST-invariant constraints. In particular, we extend a previous construction for irreducible gauge algebras to the reducible case. The gauge algebra induces two nilpotent, Grassmann-odd, mutually anticommuting BRST operators that bear structural similarities with BRST/anti-BRST theories but with shifted ghost number assignments. In both cases we show how the extended BRST algebra can be encoded into an operator master equation. A unitarizing Hamiltonian that respects the two BRST symmetries is constructed with the help of a gauge-fixing Boson. Abelian reducible theories are shown explicitly in full detail, while non-Abelian theories are worked out for the lowest reducibility stages and ghost momentum ranks.Comment: 42 pages, LaTeX. v2: New material added to Sec. 3.9-3.10, Sec. 6 and App. E. v3: Version published in Nuclear Physics B. v4: Grant number adde

Quantum Sp(2)-antibrackets and open groups

The recently presented quantum antibrackets are generalized to quantum Sp(2)-antibrackets. For the class of commuting operators there are true quantum versions of the classical Sp(2)-antibrackets. For arbitrary operators we have a generalized bracket structure involving higher Sp(2)-antibrackets. It is shown that these quantum antibrackets may be obtained from generating operators involving operators in arbitrary involutions. A recently presented quantum master equation for operators, which was proposed to encode generalized quantum Maurer-Cartan equations for arbitrary open groups, is generalized to the Sp(2) formalism. In these new quantum master equations the generalized Sp(2)-brackets appear naturally.Comment: 17 pages,Latexfile,corrected minor misprint in (78

General Triplectic Quantization

The general structure of the Sp(2) covariant version of the field-antifield quantization of general constrained systems in the Lagrangian formalism, the so called triplectic quantization, as presented in our previous paper with A.M.Semikhatov is further generalized and clarified. We present new unified expressions for the generating operators which are more invariant and which yield a natural realization of the operator V^a and provide for a geometrical explanation for its presence. This V^a operator provides then for an invariant definition of a degenerate Poisson bracket on the triplectic manifold being nondegenerate on a naturally defined submanifold. We also define inverses to nondegenerate antitriplectic metrics and give a natural generalization of the conventional calculus of exterior differential forms which e g explains the properties of these inverses. Finally we define and give a consistent treatment of second class hyperconstraints.Comment: 19 pages,latexfile,improved wedge produc

Triplectic Quantization: A Geometrically Covariant Description of the Sp(2)-symmetric Lagrangian Formalism

A geometric description is given for the Sp(2) covariant version of the field-antifield quantization of general constrained systems in the Lagrangian formalism. We develop differential geometry on manifolds in which a basic set of coordinates (`fields') have two superpartners (`antifields'). The quantization on such a triplectic manifold requires introducing several specific differential-geometric objects, whose properties we study. These objects are then used to impose a set of generalized master-equations that ensure gauge-independence of the path integral. The theory thus quantized is shown to extend to a level-1 theory formulated on a manifold that includes antifields to the Lagrange multipliers. We also observe intriguing relations between triplectic and ordinary symplectic geometry.Comment: Revised version -- our treatment in Section 5 has been extended and several pedagogical notes inserted in Sections 2--4; more references added

Canonical Transformations and Gauge Fixing in the Triplectic Quantization

We show that the generators of canonical transformations in the triplectic manifold must satisfy constraints that have no parallel in the usual field antifield quantization. A general form for these transformations is presented. Then we consider gauge fixing by means of canonical transformations in this Sp(2) covariant scheme, finding a relation between generators and gauge fixing functions. The existence of a wide class of solutions to this relation nicely reflects the large freedom of the gauge fixing process in the triplectic quantization. Some solutions for the generators are discussed. Our results are then illustrated by the example of Yang Mills theory.Comment: A new section about the cohomological approach to the extended BRST quantization has been included. Some new references were added too. Final version to appear in Nucl. Phys.B. 12 pages, LATE

BRST-anti-BRST covariant theory for the second class constrained systems. A general method and examples

The BRST-anti-BRST covariant extension is suggested for the split involution quantization scheme for the second class constrained theories. The constraint algebra generating equations involve on equal footing a pair of BRST charges for second class constraints and a pair of the respective anti-BRST charges. Formalism displays explicit Sp(2) \times Sp(2) symmetry property. Surprisingly, the the BRST-anti-BRST algebra must involve a central element, related to the nonvanishing part of the constraint commutator and having no direct analogue in a first class theory. The unitarizing Hamiltonian is fixed by the requirement of the explicit BRST-anti-BRST symmetry with a much more restricted ambiguity if compare to a first class theory or split involution second class case in the nonsymmetric formulation. The general method construction is supplemented by the explicit derivation of the extended BRST symmetry generators for several examples of the second class theories, including self--dual nonabelian model and massive Yang Mills theory.Comment: 19 pages, LaTeX, 2 examples adde

Unified Constrained Dynamics

The unified constrained dynamics is formulated without making use of the Dirac splitting of constraint classes. The strengthened, completely--closed, version of the unified constraint algebra generating equations is given. The fundamental phase variable supercommutators are included into the unified algebra as well. The truncated generating operator is defined to be nilpotent in terms of which the Unitarizing Hamiltonian is constructed.Comment: Lebedev Inst. preprint, 20 p

Non-Abelian Antibrackets

The $\Delta$-operator of the Batalin-Vilkovisky formalism is the Hamiltonian BRST charge of Abelian shift transformations in the ghost momentum representation. We generalize this $\Delta$-operator, and its associated hierarchy of antibrackets, to that of an arbitrary non-Abelian and possibly open algebra of any rank. We comment on the possible application of this formalism to closed string field theory.Comment: LaTeX, 8 pages (minor modification

On Generalized Gauge-Fixing in the Field-Antifield Formalism

We consider the problem of covariant gauge-fixing in the most general setting of the field-antifield formalism, where the action W and the gauge-fixing part X enter symmetrically and both satisfy the Quantum Master Equation. Analogous to the gauge-generating algebra of the action W, we analyze the possibility of having a reducible gauge-fixing algebra of X. We treat a reducible gauge-fixing algebra of the so-called first-stage in full detail and generalize to arbitrary stages. The associated "square root" measure contributions are worked out from first principles, with or without the presence of antisymplectic second-class constraints. Finally, we consider an W-X alternating multi-level generalization.Comment: 49 pages, LaTeX. v2: Minor changes + 1 more reference. v3,v4,v5: Corrected typos. v5: Version published in Nuclear Physics B. v6,v7: Correction to the published version added next to the Acknowledgemen