474 research outputs found
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
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
Non-Abelian Conversion and Quantization of Non-scalar Second-Class Constraints
We propose a general method for deformation quantization of any second-class
constrained system on a symplectic manifold. The constraints determining an
arbitrary constraint surface are in general defined only locally and can be
components of a section of a non-trivial vector bundle over the phase-space
manifold. The covariance of the construction with respect to the change of the
constraint basis is provided by introducing a connection in the ``constraint
bundle'', which becomes a key ingredient of the conversion procedure for the
non-scalar constraints. Unlike in the case of scalar second-class constraints,
no Abelian conversion is possible in general. Within the BRST framework, a
systematic procedure is worked out for converting non-scalar second-class
constraints into non-Abelian first-class ones. The BRST-extended system is
quantized, yielding an explicitly covariant quantization of the original
system. An important feature of second-class systems with non-scalar
constraints is that the appropriately generalized Dirac bracket satisfies the
Jacobi identity only on the constraint surface. At the quantum level, this
results in a weakly associative star-product on the phase space.Comment: LaTeX, 21 page
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