Related papers: Noncommutativity as a mapping of paths
We discuss a recent approach to quantum field theoretical path integration on noncommutative geometries which imply UV/IR regularising finite minimal uncertainties in positions and/or momenta. One class of such noncommutative geometries…
A general definition has been proposed recently of a linear connection and a metric in noncommutative geometry. It is shown that to within normalization there is a unique linear connection on the quantum plane and there is no metric.
Some fundamental aspects related with the construction of Robertson-Schr\"odinger like uncertainty principle inequalities are reported in order to provide an overall description of quantumness, separability and nonlocality of quantum…
I argue that the linearity of quantum mechanics is an emergent feature at the Planck scale, along with the manifold structure of space-time. In this regime the usual causality violation objections to nonlinearity do not apply, and nonlinear…
We consider the quasi-commutative approximation to a noncommutative geometry defined as a generalization of the moving frame formalism. The relation which exists between noncommutativity and geometry is used to study the properties of the…
We obtain direct, finite, descriptions of a renormalized quantum mechanical system with no reference to ultraviolet cutoffs and running coupling constants, in both the Hamiltonian and path integral pictures. The path integral description…
In this survey article we give basic introduction to the theory of quantum families of maps. We begin with a general look at non-commutative (or "quantum") topology. Then we formulate all our results in this language. Existence of quantum…
In this paper we develop the alternative path-integral approach to quantum mechanics. We present a resolvent of a Hamiltonian (which is Laplace transform of a evolution operator) in a form which has a sense of ``the sum over paths'' but it…
This article provides a basic introduction to some concepts of non-commutative geometry. The importance of quantum groups and quantum spaces is stressed. Canonical non-commutativity is understood as an approximation to the quantum group…
This paper presents a new `partitional' approach to understanding or interpreting standard quantum mechanics (QM). The thesis is that the mathematics (not the physics) of QM is the Hilbert space version of the math of partitions on a set…
The concept of quantization consists in replacing commutative quantities by noncommutative ones. In mathematical language an algebra of continuous functions on a locally compact topological space is replaced with a noncommutative…
A unified framework for different formulations of quantum theoery is introduced specifying what is meant by a quantum mechanical theory in general.
We survey noncommutative Choquet theory and some of its applications.
We utilize the close relation between the complex space $\textbf{C}^2$ and the real space $\textbf{R}^3$ to reformulate quantum mechanics in a manner which allows to, either or both, describe magnetic monopoles and quantize the underlying…
We introduce a notion of the noncommutative integrability within a framework of contact geometry.
We investigate the geode and some of its generalizations from the point of view on noncommutative symmetric functions.
In the last years noncommutative quantum mechanics has been investigated intensively. We consider the influence of magnetic field on decoherence of a system in the noncommutative quantum plane. Particularly, we point out a model in which…
In this review article we discuss some of the applications of noncommutative geometry in physics that are of recent interest, such as noncommutative many-body systems, noncommutative extension of Special Theory of Relativity kinematics,…
This dissertation explores various nonlinear responses that arise from the rich interplay between quantum geometry, disorder, magnetism and topology in quantum materials. In addition to presenting generalizations of quantum kinetic theory,…
Examples of repeatable procedures and maps are found in the open quantum dynamics of one qubit that interacts with another qubit. They show that a mathematical map that is repeatable can be made by a physical procedure that is not.