27 research outputs found
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
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
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
On the Geometry of the Batalin-Vilkovisky Formalism
An invariant definition of the operator of the Batalin-Vilkovisky
formalism is proposed. It is defined as the divergence of a Hamiltonian vector
field with an odd Poisson bracket (antibracket). Its main properties, which
follow from this definition, as well as an example of realization on
K\"ahlerian supermanifolds, are considered. The geometrical meaning of the
Batalin-Vilkovisky formalism is discussed.Comment: 11 pages , UGVA---DPT 1993/03--80
Functionals and the Quantum Master Equation
The quantum master equation is usually formulated in terms of functionals of
the components of mappings from a space-time manifold M into a
finite-dimensional vector space. The master equation is the sum of two terms
one of which is the anti-bracket (odd Poisson bracket) of functionals and the
other is the Laplacian of a functional. Both of these terms seem to depend on
the fact that the mappings on which the functionals act are vector-valued. It
turns out that neither this Laplacian nor the anti-bracket is well-defined for
sections of an arbitrary vector bundle. We show that if the functionals are
permitted to have their values in an appropriate graded tensor algebra whose
factors are the dual of the space of smooth functions on M, then both the
anti-bracket and the Laplace operator can be invariantly defined. Additionally,
one obtains a new anti-bracket for ordinary functionals.Comment: 21 pages, Late
Even and odd symplectic and K\"ahlerian structures on projective superspaces
Supergeneralization of \DC P(N) provided by even and odd K\"ahlerian
structures from Hamiltonian reduction are construct.Operator which
used in Batalin-- Vilkovisky quantization formalism and mechanics which are
bi-Hamiltonian under corresponding even and odd Poisson brackets are
considered.Comment: 19 page
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 -like differential operators of the first, the second
and the third orders with respect to the Grassmann derivatives. It is shown
that these -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
Algebras with Operator and Campbell--Hausdorff Formula
We introduce some new classes of algebras and estabilish in these algebras
Campbell--Hausdorff like formula. We describe the application of these
constructions to the problem of the connectivity of the Feynman graphs
corresponding to the Green functions in Quantum Fields Theory.Comment: 12 page