On the Usefulness of Modulation Spaces in Deformation Quantization
نویسنده
چکیده
We discuss the relevance to deformation quantization of Feichtinger’s modulation spaces, especially of the weighted Sjöstrand classesM s (R). These function spaces are good classes of symbols of pseudodifferential operators (observables). They have a widespread use in time-frequency analysis and related topics, but are not very well-known in physics. It turns out that they are particularly well adapted to the study of the Moyal star-product and of the star-exponential.
منابع مشابه
Infinitesimal deformation quantization of complex analytic spaces
For the physical aspects of deformation quantization we refer to the expository and survey papers [4] and [10]. Our objective is to initiate a version of global theory of quantization deformation in the category of complex analytic spaces in the same lines as the theory of (commutative) deformation. The goal of inifinitesimal theory is to do few steps towards construction of a star-product in t...
متن کاملAssociative deformations of complex analytic spaces
A theory of associative deformations is developed for general complex analytic spaces. Deformation quantization and commutative deformation are particular cases of this concept. Deformation cohomology and obstruction are studied. It is proved that any compact analytic space has a formal versal associative deformation. Mathematics Subject Classi cation (2000). 53D55, 13D10, 16S80, 81T70.
متن کاملDeformation Quantization of Almost Kähler Models and Lagrange–Finsler Spaces
Finsler and Lagrange spaces can be equivalently represented as almost Kähler manifolds endowed 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 ...
متن کاملDeformation quantization using groupoids. Case of toric manifolds
In the framework of C-algebraic deformation quantization we propose a notion of deformation groupoid which could apply to known examples e.g. Connes’ tangent groupoid of a manifold, its generalisation by Landsman and Ramazan, Rieffel’s noncommutative torus, and even Landi’s noncommutative 4-sphere. We construct such groupoid for a wide class of T-spaces, that generalizes the one given for C by ...
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 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 2009