Related papers: On the noncommutative eikonal
The Koopman-von Neumann equation describes the evolution of wavefunctions associated with autonomous ordinary differential equations and can be regarded as a quantum physics-inspired formulation of classical mechanics. The main advantage…
Since particles obey wave equations, in general one is not free to postulate that particles move on the geodesics associated with test particles. Rather, for this to be the case one has to be able to derive such behavior starting from the…
A Lie algebraic approach to the unitary transformations in Weyl quantization is discussed. This approach, being formally equivalent to the $\star$-quantization, is an extension of the classical Poisson-Lie formalism which can be used as an…
An essential prerequisite for the study of q-deformed physics are particle states in position and momentum representation. In order to relate x- and p-space by Fourier transformations the appropriate q-exponential series related to…
Motivated by the recent developments of gauge-covariant methods in the phase-space, a systematic method is presented aiming at the generalisation of the Moyal star-product to a non-Abelian gauge covariant one at any order. Such an expansion…
This is a short comment on the Moyal formula for deformation quantization. It is shown that the Moyal algebra of functions on the plane is canonically isomorphic to an algebra of matrices of infinite size.
Different approaches are compared to formulation of quantum mechanics of a particle on the curved spaces. At first, the canonical, quasi-classical and path integration formalisms are considered for quantization of geodesic motion on the…
We present the applications of methods from nonlinear local harmonic analysis in variational framework to calculations of nonlinear motions in polynomial/rational approximations (up to any order) of arbitrary n-pole fields. Our approach is…
Quantum Euclidean spaces, as Moyal deformations of Euclidean spaces, are the model examples of noncompact noncommutative manifold. In this paper, we study the quantum Euclidean space equipped with partial derivatives satisfying canonical…
The Moyal--Weyl description of quantum mechanics provides a comprehensive phase space representation of dynamics. The Weyl symbol image of the Heisenberg picture evolution operator is regular in $\hbar$. Its semiclassical expansion…
We introduce new representations to formulate quantum mechanics on noncommutative phase space, in which both coordinate-coordinate and momentum-momentum are noncommutative. These representations explicitly display entanglement properties…
Various corrections to the eikonal approximations are studied for two- and three-body nuclear collisions with the goal to extend the range of validity of this approximation to beam energies of 10 MeV/nucleon. Wallace's correction does not…
We present an explicit construction of a unitary representation of the commutator algebra satisfied by position and momentum operators on the Moyal plane.
We consider "unphysical", kinematic observables that do not commute with the constraints of a gauge system in the context of an extension of the system. We show that these observables, while not predictable, can nevertheless be said to have…
Modulo some natural generalizations to noncompact spaces, we show in this letter that Moyal planes are nonunital spectral triples in the sense of Connes. The action functional of these triples is computed, and we obtain the expected result,…
We study the metric aspect of the Moyal plane from Connes' noncommutative geometry point of view. First, we compute Connes' spectral distance associated with the natural isometric action of R^2 on the algebra of the Moyal plane A. We show…
Quantum information theory is used to analize various non-linear operations on quantum states. The universal disentanglement machine is shown to be impossible, and partial (negative) results are obtained in the state-dependent case. The…
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…
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…
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…