相关论文: Volume and Quantizations

The different roles and natures of spacetime appearing in a quantum field theory and in classical physics are analyzed implying that a quantum theory of gravitation is not necessarily a quantum theory of curved spacetime. Developing an…

We present a parallel between commutative and non-commutative polymorphisms. Our emphasis is the applications to conditional distributions from stochastic processes. In the classical case, both the measures and the positive definite kernels…

We define several new types of quantum chromatic numbers of a graph and characterise them in terms of operator system tensor products. We establish inequalities between these chromatic numbers and other parameters of graphs studied in the…

Relativistic dynamics with energy and momentum resricted to an anti-de-Sitter space is presented, specifically in the introduction of coordiate operators conjugate to such momenta. Definition of functions of these operators, their…

In this paper we will present an ongoing project which aims to use model theory as a suitable mathematical setting for studying the formalism of quantum mechanics. We will argue that this approach provides a geometric semantics for such…

The volume of the quantum mechanical state space over $n$-dimensional real, complex and quaternionic Hilbert-spaces with respect to the canonical Euclidean measure is computed, and explicit formulas are presented for the expected value of…

We discuss different proposals for the degree of polarization of quantum fields. The simplest approach, namely making a direct analogy with the classical description via the Stokes operators, is known to produce unsatisfactory results.…

This is the extended version of a talk presented at the J.W.Goethe Universitaet Frankfurt a. M. and at the same time a preview at a forthcoming extensive publication on the same subject. It is shown that there is a common background…

Let G be a rank 1 simple Lie group and M be a connected orientable aspherical tame manifold. Assume that each end of M has amenable fundamental group. There are several definitions of volume of representations of the fundamental group of M…

Following the same steps made for a scalar field in a parallel publication, we propose a class of perturbative theories of quantum gravity based on fractional operators, where the kinetic operator of the graviton is either made of…

In this paper we continue the study, started in [1], of the operatorial formulation of classical mechanics given by Koopman and von Neumann (KvN) in the Thirties. In particular we show that the introduction of the KvN Hilbert space of…

Time evolution of quantum systems is of interest in physics, in chemistry, and, more recently, in computer science. Quantum computers are suggested as one route to propagating quantum systems far more efficiently than ordinary numerical…

Quantum polyhedra constructed from angular momentum operators are the building blocks of space in its quantum description as advocated by Loop Quantum Gravity. Here we extend previous results on the semiclassical properties of quantum…

The universal enveloping algebra U(g) of a Lie algebra g acts on its representation ring R through D(R), the ring of differential operators on R. A quantised universal enveloping algebra (or "quantum group") is a deformation of a universal…

We bring together in one place some of the main results and applications from our recent works in quantum information theory, in which we have brought techniques from operator theory, operator algebras, and graph theory for the first time…

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…

The purpose of this paper is to articulate a coherent and easy-to-understand way of doing quantum mechanics in any finite-dimensional Liouville space, based on the use of Kronecker product and what we have termed the `bra-flipper' operator.…

A quantum equivalence principle is formulated by means of a gravitational phase operator which is an element of the Poincare group. This is applied to the spinning cosmic string which suggests that it may (but not necessarily) contain…

The goal of this article is to provide an overview of the current state of the art in loop quantum cosmology for three sets of audiences: young researchers interested in entering this area; the quantum gravity community in general; and,…

In this review we attempt to present an overview of some of the better known quantization techniques found in the current literature and used both by physicists and mathematicians. The treatment is more descriptive than rigorous, for we aim…