Related papers: Non-Commutative Mechanics as a modification of spa…
We study the formulation of quantum statistical mechanics in noncommutative spaces. We construct microcanonical and canonical ensemble theory in noncommutative spaces. We consider for illustration some basic and important examples in the…
Quantum mechanics in its presently known formulation requires an external classical time for its description. A classical spacetime manifold and a classical spacetime metric are produced by classical matter fields. In the absence of such…
In high-energy physics, coordinate noncommutativity represents the core idea that space itself can be quantized, as expressed through the frameworks of string theory and noncommutative field theory. Influence of such a noncommutativity on…
We consider the probabilistic description of nonrelativistic, spinless one-particle classical mechanics, and immerse the particle in a deformed noncommutative phase space in which position coordinates do not commute among themselves and…
Non-relativistic quantum mechanics is shown to emerge from classical mechanics through the requirement of a relativity principle based on special transformations acting on position and momentum uncertainties. These transformations keep the…
We consider a model of non-commutative Quantum Mechanics given by two harmonic oscillators over a non-commutative two dimensional configuration space. We study possible ways of removing the non-commutativity based on the classical limit…
Non-commutative structures were introduced, independently and around the same time, in mathematical and in condensed matter physics (see Table~1). Souriau's construction applied to the two-parameter central extension of the planar Galilei…
We consider classical and quantum mechanics related to an additional noncommutativity, symmetric in position and momentum coordinates. We show that such mechanical system can be transformed to the corresponding one which allows employment…
We formulate quantum mechanics in spacetimes with real-order fractional geometry and more general factorizable measures. In spacetimes where coordinates and momenta span the whole real line, Heisenberg's principle is proven and the…
We generalize the formulation of non-commutative quantum mechanics to three dimensional non-commutative space. Particular attention is paid to the identification of the quantum Hilbert space in which the physical states of the system are to…
Novel quantization properties related to the state vectors and the energy spectrum of a two-dimensional system of free particles are obtained in the framework of noncommutative (NC) quantum mechanics (QM) supported by the Weyl-Wigner…
We study the formulation of statistical mechanics on noncommutative classical phase space, and construct the corresponding canonical ensemble theory. For illustration, some basic and important examples are considered in the framework of…
We consider the quantum dynamics of a test particle in noncommutative space under the influence of linearized gravitational waves in the long wave-length and low-velocity limit. A prescription for quantizing the classical Hamiltonian for…
We investigate the incorporation of space noncommutativity into field theory by extending to the spectral continuum the minisuperspace action of the quantum mechanical harmonic oscillator propagator with an enlarged Heisenberg algebra. In…
The model of the position-dependent noncommutativety in quantum mechanics is proposed. We start with a given commutation relations between the operators of coordinates [x^{i},x^{j}]=\omega^{ij}(x), and construct the complete algebra of…
This paper is devoted to the construction and analysis of the Wigner functions for noncommutative quantum mechanics, their marginal distributions and star-products, following a technique developed earlier, {\it viz\/,} using the unitary…
Effects of noncommutativity are investigated in planar quantum mechanics in the coordinate representation. Generally these issues are addressed by converting to the momentum space. In the first part of the work we show noncommutative…
In a recent paper we have suggested that a formulation of quantum mechanics should exist, which does not require the concept of time, and that the appropriate mathematical language for such a formulation is noncommutative differential…
We consider a new D=2 nonrelativistic classical mechanics model providing via the Noether theorem the (2+1)-Galilean symmetry algebra with two central charges: mass m and the coupling constant k of a Chern-Simons-like term. In this way we…
In this paper noncommutative gravity is constructed as a gauge theory of the noncommutative SO(2,3) group, while the noncommutativity is canonical (constant). The Seiberg-Witten map is used to express noncommutative fields in terms of the…