相关论文: Noncommutativity and Discrete Physics

The standard lore in noncommutative physics is the use of first order variational description of a dynamical system to probe the space noncommutativity and its consequences in the dynamics in phase space. As the ultimate goal is to…

In recent years, many new developments in theoretical physics, and in practical applications rely on different techniques of noncommutative algebras. In this review, we introduce the basic concepts and techniques of noncommutative physics…

These notes are intended as an introduction to a study of applications of noncommutative calculus to quantum statistical Physics. Centered on noncommutative calculus we describe the physical concepts and mathematical structures appearing in…

A suitable unified statistical formulation of quantum and classical mechanics in a *-algebraic setting leads us to conclude that information itself is noncommutative in quantum mechanics. Specifically we refer here to an observer's…

The model of the physical system with discrete interactions is based on the postulates that (i) parameters of the physical system are defined in process of its interaction; (ii) the process of interaction is discrete. Consequently ordering…

The implications of the physical theory of quantum mechanics on the question of realism is much a subject of sustaining interest, while the background questions among physicists on how to think about all the theoretical notion and…

Time-space noncommutativity leads to quantisation of time and energy nonconservation when time is conjugate to a compact spatial direction like a circle. In this context energy is conserved only modulo some fixed unit. Such a possibility…

The standard presentation of the principles of quantum mechanics is critically reviewed both from the experimental/operational point and with respect to the request of mathematical consistency and logical economy. A simpler and more…

This paper presents a new modified quantum mechanics, Critical Complexity Quantum Mechanics, which includes a new account of wavefunction collapse. This modified quantum mechanics is shown to arise naturally from a fully discrete physics,…

Till now, the foundation of quantum physics is still mysterious. To explore the mysteries in the foundation of quantum physics, people always take it for granted that quantum processes must be some types of fields/objects on a rigid space.…

The basic premise of Quantum Mechanics, embodied in the doctrine of wave-particle duality, assigns both, a particle and a wave structure to the physical entities. The classical laws describing the motion of a particle and the evolution of a…

In this sequence of papers, noncommutative analysis is used to give a consistent axiomatic approach to a unified conceptual foundation of classical and quantum physics. The present Part I defines the concepts of observables, states and…

We study the process of observation (measurement), within the framework of a `perspectival' (`relational', `relative state') version of the modal interpretation of quantum mechanics. We show that if we assume certain features of…

Dyson published in 1990 a proof due to Feynman of the Maxwell equations. This proof is based on the assumption of simple commutation relations between position and velocity. We first study a nonrelativistic particle using Feynman formalism.…

Inspired by the discrete evolution implied by the recent work on loop quantum cosmology, we obtain a discrete time description of usual quantum mechanics viewing it as a constrained system. This description, obtained without any…

I describe a constructive foundation for Quantum Mechanics, based on the discreteness of the degrees of freedom of quantum objects and on the Principle of Relativity. Taking Einstein's historical construction of Special Relativity as a…

A consistent classical mechanics formulation is presented in such a way that, under quantization, it gives a noncommutative quantum theory with interesting new features. The Dirac formalism for constrained Hamiltonian systems is strongly…

The attempt to unify the laws of physics is approached from a discrete vision of space and time, abandoning the continuous medium paradigm that presided over the derivation of certain equations of physics-Navier-Stokes., Navier-Lam{\'e},…

To understand the foundations of quantum mechanics, we have to think carefully about how theoretical concepts are rooted in -- and limited by -- the nature of experience, as Bohr attempted to show. Geometrical pictures of physical phenomena…

A number of issues related to measurement show that self-consistency is lacking in quantum mechanics as this theory has been generally understood. Each issue is presented as a point in this paper. Each point can be resolved by incorporating…