451 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
The Generalized Moyal Nahm and Continuous Moyal Toda Equations
We present in detail a class of solutions to the Moyal Anti
Self Dual Yang Mills equations that are related to of the
generalized Moyal Nahm quations using the Ivanova-Popov ansatz. The former
yields solutions to the ASDYM/SDYM equations for arbitary gauge groups. A
further dimensional reduction yields solutions to the Moyal Anti Self Dual
Gravitational equations. The Self Dual Yang Mills /Self Dual Gravity case
requires a separate study. SU(2) and (continuous) Moyal Toda
equations are derived and solutions to the latter equations in form
are proposed via the Lax-Brockett double commutator formalism . An explicit map
taking the Moyal heavenly form (after a rotational Killing symmetry reduction)
into the SU(2) Moyal Toda field is found. Finally, the generalized Moyal Nahm
equations are conjectured that contain the continuous Moyal Toda
equation after a suitable reduction. Three different embeddings of the three
different types of Moyal Toda equations into the Moyal Nahm equations are
discussed.Comment: Revised TEX file. 31 pages. The Legendre transform between the Moyal
heavenly form and the Moyal Toda field is solve
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
Перспективи енергетичного співробітництва України та США. (The prospects of energy cooperation between Ukraine and the USA.)
У статті висвітлено історію становлення та перспективи розвитку українсько-американських відносин в енергетичій сфері як один із пріоритетів зовнішньої політики України.
(This article investigates the history of the formation and prospects of Ukraine-US relations in the energy cooperation as one of the priorities of Ukraine’s foreign policy.
Ground-state Wigner functional of linearized gravitational field
The deformation quantization formalism is applied to the linearized
gravitational field. Standard aspects of this formalism are worked out before
the ground state Wigner functional is obtained. Finally, the propagator for the
graviton is also discussed within the context of this formalism.Comment: 18 pages, no figure
Fedosov Quantization of Lagrange-Finsler and Hamilton-Cartan Spaces and Einstein Gravity Lifts on (Co) Tangent Bundles
We provide a method of converting Lagrange and Finsler spaces and their
Legendre transforms to Hamilton and Cartan spaces into almost Kaehler
structures on tangent and cotangent bundles. In particular cases, the Hamilton
spaces contain nonholonomic lifts of (pseudo) Riemannian / Einstein metrics on
effective phase spaces. This allows us to define the corresponding Fedosov
operators and develop deformation quantization schemes for nonlinear mechanical
and gravity models on Lagrange- and Hamilton-Fedosov manifolds.Comment: latex2e, 11pt, 35 pages, v3, accepted to J. Math. Phys. (2009
Gauge Theories in Noncommutative Homogeneous K\"ahler Manifolds
We construct a gauge theory on a noncommutative homogeneous K\"ahler
manifold, where we employ the deformation quantization with separation of
variables for K\"ahler manifolds formulated by Karabegov. A key point in this
construction is to obtaining vector fields which act as inner derivations for
the deformation quantization. We show that these vector fields are the only
Killing vector fields. We give an explicit construction of this gauge theory on
noncommutative and noncommutative .Comment: 27 pages, typos correcte
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