Related papers: Geometrical framework of quantization problem
The paper contains a brief review of an approach to quantum entanglement based on analysis of dynamic symmetry of systems and quantum uncertainties, accompanying the measurement of mean value of certain basic observables. The latter are…
Two classes of observables defined on the configuration space of a particle are quantized, and the effects of the Yang-Mills field are discussed in the context of geometric quantization.
We give a comprehensive review of the quantization of midisuperspace models. Though the main focus of the paper is on quantum aspects, we also provide an introduction to several classical points related to the definition of these models. We…
Ideas from deformation quantization applied to algebras with one generator lead to methods to treat a nonlinear flat connection. It provides us elements of algebras to be parallel sections. The moduli space of the parallel sections is…
Connecting ideas of geometric formulation of quantum mechanics with new results in symplectic geometry a new approach to geometrical quantization procedure is proposed. As a first result we verify that the correspondence between "classical"…
The scalar matter and gravity are unified into the geometric scalar matter and quantized. The quantum with a definite 3-metric has definite energy but does not have well-defined momentum. The quantum theory resolves singularities.
A geometric quantization of a K\"{a}hler manifold, viewed as a symplectic manifold, depends on the complex structure compatible with the symplectic form. The quantizations form a vector bundle over the space of such complex structures.…
Standard particle theory is based on quantized matter embedded in a classical geometry. Here, a complementary model is proposed, based on classical matter -- massive bodies, without quantum properties -- embedded in a quantum geometry. It…
Based on a more careful canonical analysis, we motivate a reduced quantization - in the sense of superspace quantization - of slightly inhomogeneous cosmology in place of the Dirac quantization in the existing literature, and provide it in…
By means of simple models in a flat spacetime manifold we examine some of the issues that arise when quantizing interacting quantum fields in multi-metric backgrounds. In particular we investigate the maintenance of a causal structure in…
The characterization of the quantum ensemble is a fundamental issue in quantum information theory and foundations. The ensemble is also useful for various quantum information processing. To characterize the quantum ensemble, in this…
We survey decades of research identifying the (co)homology of configuration spaces with Lie algebra (co)homology. The different routes to this one proto-theorem offer genuinely different explanations of its truth, and we attempt to convey…
We examine a few problems of enumerative geometry and present their solutions in the framework of deformed (quantum) cohomology rings.
The quantization of the gravitational field is discussed within the exact uncertainty approach. The method may be described as a Hamilton-Jacobi quantization of gravity. It differs from previous approaches that take the classical…
These notes of a course given at IRMA in April 2009 cover some aspects of the representation theory of fundamental groups of manifolds of dimension at most 3 in compact Lie groups, mainly $\su$. We give detailed examples, develop the…
We introduce the notion of geometric pseudo-quantisation based on geometric quantisation with a weakened curvature condition. We show how such a structure arises naturally from simple deformations of the symplectic structure and pullbacks…
A unified framework for different formulations of quantum theoery is introduced specifying what is meant by a quantum mechanical theory in general.
This is an introduction to quantum gravity, aimed at a fairly general audience and concentrating on what have historically two main approaches to quantum gravity: the covariant and canonical programs (string theory is not covered). The…
We compare the respective efficiencies of three quantization methods (group theoretical, coherent state and geometric) by quantizing the dynamics of a free massive particle in two-dimensional de Sitter space. For each case we consider the…
General Relativity describes gravity in geometrical terms. This suggests that quantizing such theory is the same as quantizing geometry. The subject can therefore be called quantum geometry and one may think that mathematicians are…