Related papers: Physical Framework of Quantization Problem
We apply the topological quantization method to some gravitational fields which can be represented as generalized harmonic maps. This representation extends the well-known concept of harmonic maps and allows us to describe some solutions to…
The problem of constructing a quantum theory of gravity is considered from a novel viewpoint. It is argued that any consistent theory of gravity should incorporate a relational character between the matter constituents of the theory. In…
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.
The paper presents an extension of the geometric quantization procedure to integrable, big-isotropic structures. We obtain a generalization of the cohomology integrality condition, we discuss geometric structures on the total space of the…
A unified framework for different formulations of quantum theoery is introduced specifying what is meant by a quantum mechanical theory in general.
We argue about a conceptual approach to quantum formalism. Starting from philosophical conjectures (Platonism, Idealism and Realism) as basic ontic elements (namely: math world, data world, and state of matter), we will analyze the quantum…
We give a very concise review of the group field theory formalism for non-perturbative quantum gravity, a higher dimensional generalisation of matrix models. We motivate it as a simplicial and local realisation of the idea of 3rd…
In this tenth paper of the series we aim at showing that our formalism, using the Wigner-Moyal Infinitesimal Transformation together with classical mechanics, endows us with the ways to quantize a system in any coordinate representation we…
We consider a geometrization, i.e., we identify geometrical structures, for the space of density states of a quantum system. We also provide few comments on a possible application of this geometrization for composite systems.
The multilevel geometrically--covariant generalization of the field--antifield BV--formalism is suggested. The structure of quantum generating equations and hypergauge conditions is studied in details. The multilevel formalism is…
We show how to formulate physical theory taking as a starting point the set of states (geometric approach). We discuss the relation of this formulation to the conventional approach to classical and quantum mechanics and the theory of…
We review the basic elements of the geometrical formalism for description of gauge fields and the theory of invariant connections, and their applications to the coset space dimensional reduction of Yang-Mills theories. We also discuss the…
We introduce a new "positive formalism" for encoding quantum theories in the general boundary formulation, somewhat analogous to the mixed state formalism of the standard formulation. This makes the probability interpretation more natural…
A new, configuration-space picture of a formalism of group quantization, the GAQ formalism, is presented in the context of a previous, algebraic generalization. This presentation serves to make a comprehensive discussion in which other…
A discussion of the meaning of a physical concept cannot be separated from discussion of the conditions for its ideal measurement. We assert that quantization is no more than the invocation of the quantum of action in the explanation of…
The aim of this article is to study the functorial properties of the ``formal geometric quantization'' procedure which is defined for non-compact Hamiltonian manifolds (when the moment map is proper). For this purpose, we introduce a…
A geometric framework for describing quantum particles on a possibly curved background is proposed. Natural constructions on certain distributional bundles (`quantum bundles') over the spacetime manifold yield a quantum ``formalism'' along…
This is an overview of higher structural constructions in physics. The main motivations of our current attempt are as follows: (i) to provide a brief introduction to derived algebraic geometry, (ii) to understand how derived objects…
In this paper a system-oriented formalism of Quantum Information Processing is presented. Its form resembles that of standard signal processing, although further complexity is added in order to describe pure quantum-mechanical effects and…
Suggestions concerning the generalization of the geometric quantization to the case of nonlinear field theories are given. Results for the Liouville field theory are presented.