282 research outputs found
Deformation Quantization of Almost Kahler Models and Lagrange-Finsler Spaces
Finsler and Lagrange spaces can be equivalently represented as almost Kahler
manifolds enabled with a metric compatible canonical distinguished connection
structure generalizing the Levi Civita connection. The goal of this paper is to
perform a natural Fedosov-type deformation quantization of such geometries. All
constructions are canonically derived for regular Lagrangians and/or
fundamental Finsler functions on tangent bundles.Comment: the latex 2e variant of the manuscript accepted for JMP, 11pt, 23
page
BRST quantization of quasi-symplectic manifolds and beyond
We consider a class of \textit{factorizable} Poisson brackets which includes
almost all reasonable Poisson structures. A particular case of the factorizable
brackets are those associated with symplectic Lie algebroids. The BRST theory
is applied to describe the geometry underlying these brackets as well as to
develop a deformation quantization procedure in this particular case. This can
be viewed as an extension of the Fedosov deformation quantization to a wide
class of \textit{irregular} Poisson structures. In a more general case, the
factorizable Poisson brackets are shown to be closely connected with the notion
of -algebroid. A simple description is suggested for the geometry underlying
the factorizable Poisson brackets basing on construction of an odd Poisson
algebra bundle equipped with an abelian connection. It is shown that the
zero-curvature condition for this connection generates all the structure
relations for the -algebroid as well as a generalization of the Yang-Baxter
equation for the symplectic structure.Comment: Journal version, references and comments added, style improve
Higher order relations in Fedosov supermanifolds
Higher order relations existing in normal coordinates between affine
extensions of the curvature tensor and basic objects for any Fedosov
supermanifolds are derived. Representation of these relations in general
coordinates is discussed.Comment: 11 LaTex pages, no figure
Scalar Casimir Energies of Tetrahedra
New results for scalar Casimir self-energies arising from interior modes are
presented for the three integrable tetrahedral cavities. Since the eigenmodes
are all known, the energies can be directly evaluated by mode summation, with a
point-splitting regulator, which amounts to evaluation of the cylinder kernel.
The correct Weyl divergences, depending on the volume, surface area, and the
corners, are obtained, which is strong evidence that the counting of modes is
correct. Because there is no curvature, the finite part of the quantum energy
may be unambiguously extracted. Dirichlet and Neumann boundary conditions are
considered and systematic behavior of the energy in terms of geometric
invariants is explored.Comment: Talk given at QFEXT 1
Symplectic geometries on supermanifolds
Extension of symplectic geometry on manifolds to the supersymmetric case is
considered. In the even case it leads to the even symplectic geometry (or,
equivalently, to the geometry on supermanifolds endowed with a non-degenerate
Poisson bracket) or to the geometry on an even Fedosov supermanifolds. It is
proven that in the odd case there are two different scalar symplectic
structures (namely, an odd closed differential 2-form and the antibracket)
which can be used for construction of symplectic geometries on supermanifolds.Comment: LaTex, 1o pages, LaTex, changed conten
Direct Detection of Electroweak-Interacting Dark Matter
Assuming that the lightest neutral component in an SU(2)L gauge multiplet is
the main ingredient of dark matter in the universe, we calculate the elastic
scattering cross section of the dark matter with nucleon, which is an important
quantity for the direct detection experiments. When the dark matter is a real
scalar or a Majorana fermion which has only electroweak gauge interactions, the
scattering with quarks and gluon are induced through one- and two-loop quantum
processes, respectively, and both of them give rise to comparable contributions
to the elastic scattering cross section. We evaluate all of the contributions
at the leading order and find that there is an accidental cancellation among
them. As a result, the spin-independent cross section is found to be
O(10^-(46-48)) cm^2, which is far below the current experimental bounds.Comment: 19 pages, 7 figures, published versio
A zeta function approach to the relation between the numbers of symmetry planes and axes of a polytope
A derivation of the Ces\`aro-Fedorov relation from the Selberg trace formula
on an orbifolded 2-sphere is elaborated and extended to higher dimensions using
the known heat-kernel coefficients for manifolds with piecewise-linear
boundaries. Several results are obtained that relate the coefficients, ,
in the Shephard-Todd polynomial to the geometry of the fundamental domain. For
the 3-sphere we show that is given by the ratio of the volume of the
fundamental tetrahedron to its Schl\"afli reciprocal.Comment: Plain TeX, 26 pages (eqn. (86) corrected
-SDYM fields and heavenly spaces: II. Reductions of the -SDYM system
Reductions of self-dual Yang-Mills (SDYM) system for -bracket Lie
algebra to the Husain-Park (HP) heavenly equation and to
sl(N,{\boldmath{C}) SDYM equation are given. An example of a sequence of
chiral fields () tending for to a curved heavenly
space is found.Comment: 18 page
Cohomologies of the Poisson superalgebra
Cohomology spaces of the Poisson superalgebra realized on smooth
Grassmann-valued functions with compact support on ($C^{2n}) are
investigated under suitable continuity restrictions on cochains. The first and
second cohomology spaces in the trivial representation and the zeroth and first
cohomology spaces in the adjoint representation of the Poisson superalgebra are
found for the case of a constant nondegenerate Poisson superbracket for
arbitrary n>0. The third cohomology space in the trivial representation and the
second cohomology space in the adjoint representation of this superalgebra are
found for arbitrary n>1.Comment: Comments: 40 pages, the text to appear in Theor. Math. Phys.
supplemented by computation of the 3-rd trivial cohomolog
Weyl-Underhill-Emmrich quantization and the Stratonovich-Weyl quantizer
Weyl-Underhill-Emmrich (WUE) quantization and its generalization are
considered. It is shown that an axiomatic definition of the Stratonovich-Weyl
(SW) quantizer leads to severe difficulties. Quantization on the cylinder
within the WUE formalism is discussed.Comment: 15+1 pages, no figure
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