Geometric Quantization of Vector Bundles and the Correspondence with Deformation Quantization
نویسندگان
چکیده
منابع مشابه
Geometric Quantization of Vector Bundles
I repeat my definition for quantization of a vector bundle. For the cases of Töplitz and geometric quantization of a compact Kähler manifold, I give a construction for quantizing any smooth vector bundle which depends functorially on a choice of connection on the bundle.
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Using the classification of formal deformation quantizations, and the formal, algebraic index theorem, I give a simple proof as to which formal deformation quantization (modulo isomorphism) is derived from a given geometric quantization.
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Motivated by deformation quantization, we consider in this paper -algebras A over rings C = R(i), where R is an ordered ring and i = −1, and study the deformation theory of projective modules over these algebras carrying the additional structure of a (positive) A-valued inner product. For A = C(M), M a manifold, these modules can be identified with Hermitian vector bundles E overM . We show tha...
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The quantization of vector bundles is defined. Examples are constructed for the well controlled case of equivariant vector bundles over compact coadjoint orbits. (Coadjoint orbits are symplectic spaces with a transitive, semisimple symmetry group.) In preparation for the main result, the quantization of coadjoint orbits is discussed in detail. This subject should not be confused with the quanti...
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Consider a fiber bundle in which the total space, the base space and the fiber are all symplectic manifolds. We study the relations between the quantization of these spaces. In particular, we discuss the geometric quantization of a vector bundle, as oppose to a line bundle, over the base space that recovers the standard geometric quantization of the total space.
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ژورنال
عنوان ژورنال: Communications in Mathematical Physics
سال: 2000
ISSN: 0010-3616
DOI: 10.1007/s002200000308