A Ring-Theorist’s Description of Fedosov Quantization
نویسنده
چکیده
We present a formal, algebraic treatment of Fedosov’s argument that the coordinate algebra of a symplectic manifold has a deformation quantization. His remarkable formulas are established in the context of affine symplectic algebras.
منابع مشابه
Fedosov ∗-products and quantum momentum maps
The purpose of the paper is to study various aspects of star products on a symplectic manifold related to the Fedosov method. By introducing the notion of “quantum exponential maps”, we give a criterion characterizing Fedosov connections. As a consequence, a geometric realization is obtained for the equivalence between an arbitrary ∗-product and a Fedosov one. Every Fedosov ∗-product is shown t...
متن کاملFedosov supermanifolds: II. Normal coordinates
The formulation of fundamental physical theories, classical as well as quantum ones, by differential geometric methods nowadays is well established and has a great conceptual virtue. Probably, the most prominent example is the formulation of general relativity on Riemannian manifolds, i.e., the geometrization of the gravitational force; no less important is the geometric formulation of gauge fi...
متن کاملFedosov 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 Kähler 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 d...
متن کاملFedosov Deformation Quantization as a BRST Theory
The relationship is established between the Fedosov deformation quantization of a general symplectic manifold and the BFV-BRST quantization of constrained dynamical systems. The original symplectic manifold M is presented as a second class constrained surface in the fibre bundle T * ρ M which is a certain modification of a usual cotangent bundle equipped with a natural symplectic structure. The...
متن کاملFe b 20 06 Abelian connection in Fedosov deformation quantization . I . The 2 – dimensional phase space
General properties of Abelian connection in Fedosov deformation quantization are investigated. Criteria of being a finite series for an Abelian connection are presented. Conditions for different symplectic connections to generate the same correction to the Abelian connection are given. A proof that in 2–dimensional case the Abelian connection is an ifinite series is done. A class of symplectic ...
متن کامل