Related papers: Geometric Quantization
Classical mechanics has a natural mathematical setting in symplectic geometry and it may be asked if the same is true for quantum mechanics. More precisely, is it possible to capture certain quantum idiosyncrasies within the symplectic…
These notes give an introduction to the quantization procedure called geometric quantization. It gives a definition of the mathematical background for its understanding and introductions to classical and quantum mechanics, to differentiable…
Quantum mechanics is among the most important and successful mathematical model for describing our physical reality. The traditional formulation of quantum mechanics is linear and algebraic. In contrast classical mechanics is a geometrical…
We review the definition of geometric quantization, which begins with defining a mathematical framework for the algebra of observables that holds equally well for classical and quantum mechanics. We then discuss prequantization, and go into…
Geometric Quantization is a term used to describe a wide collection of techniques dating back to the 1960s in the work of Kirillov, Kostant, and Souriau, which take symplectic manifolds and produce complex vector spaces. The name comes from…
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.
The basic elements of the geometric approach to a consistent quantization formalism are summarized, with reference to the methods of the old quantum mechanics and the induced representations theory of Lie groups. A possible relationship…
A comparison on some facts concerning the geometric quantization of symplectic manifolds is presented here. Criticism, facts and improvements on the sophisticated theory of geometric quantization are presented touching briefly, all the…
The method of geometric quantization is applied to a particle moving on an arbitrary Riemannian manifold $Q$ in an external gauge field, that is a connection on a principal $H$-bundle $N$ over $Q$. The phase space of the particle is a…
Geometric quantization of a Poisson manifold need not imply quantization of its symplectic leaves. We provide the leafwise geometric quantization of a Poisson manifold, seen as a foliated one, whose quantum algebra restricted to each leaf…
The geometric quantization problem is considered from the point of view of the Davies and Lewis approach to quantum mechanics. The influence of the measuring device is accounted in the classical and quantum case and it is shown that the…
The geometro-stochastic method of quantization provides a framework for quantum general relativity, in which the principal frame bundles of local Lorentz frames that underlie the fibre-theoretical approach to classical general relativity…
The formulation of Geometric Quantization contains several axioms and assumptions. We show that for real polarizations we can generalize the standard geometric quantization procedure by introducing an arbitrary connection on the…
Phase space is the state space of classical mechanics, and this manifold is normally endowed only with a symplectic form. The geometry of quantum mechanics is necessarily more complicated. Arguments will be given to show that augmenting the…
Geometric quantization is a natural way to construct quantum models starting from classical data. In this work, we start from a symplectic vector space with an inner product and -- using techniques of geometric quantization -- construct the…
Different approaches are compared to formulation of quantum mechanics of a particle on the curved spaces. At first, the canonical, quasi-classical and path integration formalisms are considered for quantization of geodesic motion on the…
The metric known to be relevant for standard quantization procedures receives a natural interpretation and its explicit use simultaneously gives both physical and mathematical meaning to a (coherent-state) phase-space path integral, and at…
The paper presents shortly the geometric approach to the problem of a general quantization formalism, both physically meaningful and mathematically consistent.
The unsatisfactory status of the search for a consistent and predictive quantization of gravity is taken as motivation to study the question whether geometrical laws could be more fundamental than quantization procedures. In such an…
In this paper we investigate the possibility of constructing a complete quantization procedure consisting of geometric and deformation quantization. The latter assigns a noncommutative algebra to a symplectic manifold, by deforming the…