相关论文: Physical Framework of Quantization Problem

This essay constitutes a review of the information geometric approach to renormalization developed in the recent works of B\'eny and Osborne as well as a detailed work-through of some of their contents. A noncommutative generalization of…

We propose a generalization of quantization as a categorical way. For a fixed Poisson algebra quantization categories are defined as subcategories of R-module category with the structure of classical limits. We construct the generalized…

We develop a kind of quantum formalism (Hilbert space probabilistic calculus) for measurements performed over cognitive (in particular, conscious) systems. By using this formalism we could predict averages of cognitive observables.…

Over the past five years, there has been significant progress on the problem of quantization of diffeomorphism covariant field theories with {\it local} degrees of freedom. The absence of a background space-time metric in these theories…

In the context of formal deformation quantization, we provide an elementary argument showing that any universal quantization formula necessarily involves graphs with wheels.

In this article we present a generalization of a Leibniz's geometrical theorem and an application of it.

Two strategies for constructing general geometric operators in all dimensional loop quantum gravity are proposed. The different constructions are mainly come from the two different regularization methods for the de-densitized dual momentum,…

The problem of quantization of general relativity is considered in the framework of noncommutative differential geometry. Operator analogues for interval, scalar curvature, values of the Einstein tensor are proposed. Quantum measurements of…

A possible way toward the quantization of a weak gravitational field inspired by the imaginary-time field theory is discussed. The analogies of the general relativity in the canonical formulation with the thermodynamic geometry and…

An attempt is made to formulate quantum mechanics (QM) in physical rather than in mathematical terms. It is argued that the appropriate conceptual framework for QM is "contextual objectivity", which includes an objective definition of the…

This note gives an overview of the BV formalism in its various incarnations and applications.

This article provides a simple geometric interpretation of the quadratic formula. The geometry helps to demystify the formula's complex appearance and casts it into a much simpler existence, thus potentially benefits early algebra students.

While canonical quantization solves many problems there are some problems where it fails. A close examination of the classical/quantum connection leads to a new connection that permits quantum and classical realms to coexist, as is the case…

The purpose of this article is to draw attention to some fundamental issues in General Relativity. It is argued that these deep issues cannot be resolved within the standard approach to general relativity that considers {\em every} solution…

In this paper we give a streamlined overview of some of the recent constructions provided with K.-H. Neeb, G. \'Olafsson and collaborators for a new geometric approach to Algebraic Quantum Field Theory (AQFT). Motivations, fundamental…

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…

Quantization with coherent states allows to " quantize " any space X of parameters. In the case where X is a phase space, this leads to the usual quantum mechanics. But the procedure is much more general, and does not require a symplectic,…

A perturbative formulation of algebraic field theory is presented, both for the classical and for the quantum case, and it is shown that the relation between them may be understood in terms of deformation quantization.

The new approach to quantize the gravity based on the notion of differential algebra is suggested. It is shown that the differential geometry of this object can not be described in terms of points. The spatialization procedure giving rise…

An algebraic formulation of general relativity is proposed. The formulation is applicable to quantum gravity and noncommutative space. To investigate quantum gravity we develop the canonical formalism of operator geometry, after…