Cartan connections and natural and projectively equivariant quantizations
نویسندگان
چکیده
منابع مشابه
Cartan Connections and Natural and Projectively Equivariant Quantizations
In this paper, we analyse the question of existence of a natural and projectively equivariant symbol calculus, using the theory of projective Cartan connections. We establish a close relationship between the existence of such a natural symbol calculus and the existence of an sl(m+1,R)equivariant calculus over R in the sense of [15, 1]. Moreover we show that the formulae that hold in the non-cri...
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The existence of a natural and projectively equivariant quantization in the sense of Lecomte [20] was proved recently by M. Bordemann [4], using the framework of Thomas-Whitehead connections. We give a new proof of existence using the notion of Cartan projective connections and we obtain an explicit formula in terms of these connections. Our method yields the existence of a projectively equivar...
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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...
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The concept of conformally equivariant quantizations was introduced by Duval, Lecomte and Ovsienko in [8] for manifolds endowed with flat conformal structures. They obtained results of existence and uniqueness (up to normalization) of such a quantization procedure. A natural generalization of this concept is to seek for a quantization procedure, over a manifold M , that depends on a pseudo-Riem...
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Theorem 1. Let T 2 be the two dimensional torus. Then for any positive integer m there is a complete torsion free projectively flat connection, ∇, on T 2 such that for any point p ∈ T 2 there is a point q ∈ T 2 with the property that any broken ∇-geodesic between p and q has at least m breaks. Moreover if T 2 is viewed as a Lie group in the usual manner, this connection is invariant under trans...
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ژورنال
عنوان ژورنال: Journal of the London Mathematical Society
سال: 2007
ISSN: 0024-6107
DOI: 10.1112/jlms/jdm030