Geometric Quantization from a Coherent State Viewpoint
نویسنده
چکیده
A fully geometric procedure of quantization that utilizes a natural and necessary metric on phase space is reviewed and briefly related to the goals of the program of geometric quantization. Introduction and Background Purpose and achievements The goal of the present work is to present a conceptually simple, geometric prescription for quantization. Such a goal has been, and continues to be, the subject of a number of research efforts. In the present paper we shall look at the problems faced by this program from the point of view of coherent states. It will be our conclusion that the symplectic geometry of classical mechanics, augmented by a natural, and even necessary, metric on the classical phase space, are the only essential ingredients to provide a quantization scheme that is fully geometric in character and one that can be expressed in a coordinate-free form. In a surprising sense we shall see that coherent states—far from being optional—are in fact an automatic consequence of this process of quantization. It is fair to say at the outset that we will have very
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