146 research outputs found
Odd Invariant Semidensity and Divergence-like Operators on an Odd Symplectic Superspace
The divergence-like operator on an odd symplectic superspace which acts
invariantly on a specially chosen odd vector field is considered. This operator
is used to construct an odd invariant semidensity in a geometrically clear way.
The formula for this semidensity is similar to the formula of the mean
curvature of hypersurfaces in Euclidean space.Comment: 18 pages, TeX fil
A Note on Semidensities in Antisymplectic Geometry
We revisit Khudaverdian's geometric construction of an odd nilpotent operator
\Delta_E that sends semidensities to semidensities on an antisymplectic
manifold. We find a local formula for the \Delta_E operator in arbitrary
coordinates and we discuss its connection to Batalin-Vilkovisky quantization.Comment: 11 pages, LaTeX. v2: Added eqs. (4.1), (6.3), (6.4) & (6.5). v3: Sec.
6 expanded and ref. added. v4: Included a proof of the main statement in the
appendices. v5: Flipped the sign convention for \nu^{(2)}. v6: Stylistic
change
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
Laplacians in Odd Symplectic Geometry
We consider odd Laplace operators arising in odd symplectic geometry.
Approach based on semidensities (densities of weight 1/2) is developed. The
role of semidensities in the Batalin--Vilkovisky formalism is explained. In
particular, we study the relations between semidensities on an odd symplectic
supermanifold and differential forms on a purely even Lagrangian submanifold.
We establish a criterion of ``normality'' of a volume form on an odd symplectic
supermanifold in terms of the canonical odd Laplacian acting on semidensities.Comment: LaTeX2e, 19 page
Batalin--Vilkovisky Formalism and Odd Symplectic Geometry
It is a review of some results in Odd symplectic geometry related to the
Batalin-Vilkovisky FormalismComment: plain TeX, 39 pages, no figure
Geometry of differential operators, odd Laplacians, and homotopy algebras
We give a complete description of differential operators generating a given
bracket. In particular we consider the case of Jacobi-type identities for odd
operators and brackets. This is related with homotopy algebras using the
derived bracket construction.
(Based on a talk at XXII Workshop on Geometric Methods in Physics at
Bialowieza)Comment: 13 pages; LaTe
Linear Odd Poisson Bracket on Grassmann Variables
A linear odd Poisson bracket (antibracket) realized solely in terms of
Grassmann variables is suggested. It is revealed that the bracket, which
corresponds to a semi-simple Lie group, has at once three Grassmann-odd
nilpotent -like differential operators of the first, the second and the
third orders with respect to Grassmann derivatives, in contrast with the
canonical odd Poisson bracket having the only Grassmann-odd nilpotent
differential -operator of the second order. It is shown that these
-like operators together with a Grassmann-odd nilpotent Casimir
function of this bracket form a finite-dimensional Lie superalgebra.Comment: 7 pages, LATEX. Relation (34) is added and the rearrangement
necessary for publication in Physics Letters B is mad
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