The Projective Quantization
نویسنده
چکیده
Introduction. Let VecR be the Lie algebra of smooth vector fields on R. In this talk we will survey some results concerning the action of VecR on modules of differential operators. To begin with, let σ be the two-sided action of VecR on the associative algebra Diff R of smooth differential operators on R: σ(X)T := X ◦ T − T ◦X. This is a derivation action which preserves the order filtration Diff R. The associated subquotients are the symbol modules:
منابع مشابه
فرمولبندی هندسی کوانتش تغییرشکل برزین
In this paper we try to formulate the Berezin quantization on projective Hilbert space P(H) and use its geometric structure to construct a correspondence between a given classical theory and a given quantum theory. It wil be shown that the star product in berezin quantization is equivalent to the Posson bracket on coherent states manifold M, embodded in P(H), and the Berezin method is used to...
متن کاملExistence of Natural and Conformally Invariant Quantizations of Arbitrary Symbols
A quantization over a manifold can be seen as a way to construct a differential operator with prescribed principal symbol. The map from the space of principal symbols to the space of differential operators is moreover required to be a linear bijection. It is known that there is in general no natural quantization procedure. However, considering manifolds endowed with additional structures, such ...
متن کاملDeformation quantization of algebraic varieties
The paper is devoted to peculiarities of the deformation quantization in the algebro-geometric context. A direct application of the formality theorem to an algebraic Poisson manifold gives a canonical sheaf of categories deforming coherent sheaves. The global category is very degenerate in general. Thus, we introduce a new notion of a semiformal deformation, a replacement in algebraic geometry ...
متن کاملThe Two Dimensional Hannay-berry Model Shamgar Gurevich and Ronny Hadani
The main goal of this paper is to construct the Hannay-Berry model of quantum mechanics, on a two dimensional symplectic torus. We construct a simultaneous quantization of the algebra of functions and the linear symplectic group Γ = SL2(Z). We obtain the quantization via an action of Γ on the set of equivalence classes of irreducible representations of Rieffel‘s quantum torus A~. For ~ ∈ Q this...
متن کاملFe b 20 09 Space of Kähler metrics ( V ) — Kähler quantization
We prove the convergence of geodesic distance during the quantization of the space of Kähler potentials. As applications, this provides alternative proofs of certain inequalities about the K-energy functional in the projective case.
متن کاملExistence of Natural and Projectively Equivariant Quantizations
We study the existence of natural and projectively equivariant quantizations for differential operators acting between order 1 vector bundles over a smooth manifold M . To that aim, we make use of the Thomas-Whitehead approach of projective structures and construct a Casimir operator depending on a projective Cartan connection. We attach a scalar parameter to every space of differential operato...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2006