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We consider a model of classical noncommutative particle in an external electromagnetic field. For this model, we prove the existence of generalized gauge transformations. Classical dynamics in Hamiltonian and Lagrangian form is discussed,…
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 analogy with conventional quantum mechanics, non-commutative quantum mechanics is formulated as a quantum system on the Hilbert space of Hilbert-Schmidt operators acting on non-commutative configuration space. It is argued that the…
We give an introductory review of quantum physics on the noncommutative spacetime called the Groenewold-Moyal plane. Basic ideas like star products, twisted statistics, second quantized fields and discrete symmetries are discussed. We also…
We present a unified approach to representations of quantum mechanics on noncommutative spaces with general constant commutators of phase-space variables. We find two phases and duality relations among them in arbitrary dimensions.…
Noncommutative field theories are a class of theories beyond the standard model of elementary particle physics. Their importance may be summarized in two facts. Firstly as field theories on noncommutative spacetimes they come with natural…
We propose an alternative interpretation for the meaning of noncommutativity of the string-inspired field theories and quantum mechanics. Arguments are presented to show that the noncommutativity generated in the stringy context should be…
Noncommutative quantum mechanics can be considered as a first step in the construction of quantum field theory on noncommutative spaces of generic form, when the commutator between coordinates is a function of these coordinates. In this…
The motion of neutral particles with magnetic moments in an inhomogeneous magnetic field is described in a quantum mechanical framework. The validity of the semi-classical approximations which are generally used to describe these phenomena…
In this work quantum physics in noncommutative spacetime is developed. It is based on the work of Doplicher et al. which allows for time-space noncommutativity. The Moyal plane is treated in detail. In the context of noncommutative quantum…
This paper considers a generalization of the notion of quantum observables in ontological models of quantum mechanics. Within this framework it is possible to construct physical models where quantum noncommutativity can arise dynamically.…
The non-individuals interpretation of quantum mechanics is presented with the aim of clarifying it and highflying some of its salient features. Alternative formulations of it are proposed and examined.
This is a brief review where some basic elements of non-commutative geometry are given. The rules and ingredients that enter in the construction of the standard model and grand unification models in non-commutative geometry are summarized.…
The first renormalisable quantum field theories on non-commutative space have been found recently. We review this rapidly growing subject.
A reinterpretation of noncommutativity as a mapping of paths is proposed at the level of quantum mechanics.
We examine the behaviour of charged particles in homogeneous, constant and/or oscillating magnetic fields in the non-relativistic approximation. A special role of the geometric center of the particle trajectory is elucidated. In quantum…
We consider electrodynamics on a noncommutative spacetime using the enveloping algebra approach and perform a non-relativistic expansion of the effective action. We obtain the Hamiltonian for quantum mechanics formulated on a canonical…
The extreme electromagnetic or gravitational fields associated with some astrophysical objects can give rise to macroscopic effects arising from the physics of the quantum vacuum. Therefore, these objects are incredible laboratories for…
We study some basic and interesting quantum mechanical systems in dynamical noncommutative spaces in which the space- space commutation relations are position dependent. It is observed that the fundamental objects in the dynamical…
We review a possible framework for (non)linear quantum theories, into which linear quantum mechanics fits as well, and discuss the notion of ``equivalence'' in this setting. Finally, we draw the attention to persisting severe problems of…