Related papers: Coordinate noncommutativity as low energy effectiv…
We prove that the Moyal product is covariant under linear affine spacetime transformations. From the covariance law, by introducing an $(x,\Theta)$-space where the spacetime coordinates and the noncommutativity matrix components are on the…
Coarse-graining is central to reducing dimensionality in molecular dynamics, and is typically characterized by a mapping which projects the full state of the system to a smaller class of variables. While extensive literature has been…
We establish a lower bound on the quantum coherence of an arbitrary quantum state in arbitrary dimension, using a noncommutativity estimator of an arbitrary observable of sub-unit norm, where the estimator is the commutator of the…
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…
When we have noncommutativity among coordinates (or conjugate momenta), we consider Wigner's formulation of quantum mechanics, including a new derivation of path integral formula. We also propose the Moyal star product based on the Dirac…
A methodology for handling block-to-block coupling of nonconforming, multiblock summation-by-parts finite difference methods is proposed. The coupling is based on the construction of projection operators that move a finite difference grid…
A nonperturbative quantization procedure based on a nonassociative decomposition of quantum field operators on nonassociative constituents is considered. It is shown that such approach gives rise to quantum corrections by calculations of…
We consider various modifications of the Weyl-Moyal star-product, in order to obtain a finite range of nonlocality. The basic requirements are to preserve the commutation relations of the coordinates as well as the associativity of the new…
We present a formulation in a curved background of noncommutative mechanics, where the object of noncommutativity $\theta^{\mu\nu}$ is considered as an independent quantity having a canonical conjugate momentum. We introduced a…
In this letter, firstly, the Schr$\ddot{o}$dinger equation on noncommutative phase space is given by using a generalized Bopp's shift. Then the anomaly term of commutator of arbitrary physical observable operators on noncommutative phase…
We introduce a notion of the noncommutative integrability within a framework of contact geometry.
We survey noncommutative spacetimes with coordinates being enveloping algebras of Lie algebras. We also explain how to do differential geometry on noncommutative spaces that are obtained from commutative ones via a Moyal-product type…
Exploiting the relative entropy of coherence, we isolate the coherent contribution in the energetics of a driven non-equilibrium quantum system. We prove that a division of the irreversible work can be made into a coherent and incoherent…
We investigate the effects of noncommutativity between the position-position, position-momentum and momentum-momentum of a phase space corresponding to a modified cosmological model. We show that the existence of such noncommutativity…
Essential to QCD applications of the operator product expansion, etc., is a knowledge of those operators that mix with gauge-invariant operators. A standard theorem asserts that the renormalization matrix is triangular: Gauge-invariant…
The gauge covariance of the wave function phase factor in noncommutative quantum mechanics (NCQM) is discussed. We show that the naive path integral formulation and an approach where one shifts the coordinates of NCQM in the presence of a…
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…
Noncommutativity of observables is a central feature of quantum physics. It plays a fundamental role in the formulation of the uncertainty principle for complementary variables and strongly affects the laws of thermodynamics for systems…
We prove that, in the setting of noncommutative differential geometry, a system of higher order connections is equivalent to a suitable generalization of the notion of phase space quantization (in the sense of Moyal star products on the…
Non-commutative quantum mechanics can be viewed as a quantum system represented in the space of Hilbert-Schmidt operators acting on non-commutative configuration space. Within this framework an unambiguous definition can be given for the…