An extensively tacit understandings of equivalency between the deformed HeisenbergWeyl algebra in noncommutative space and the undeformed Heisenberg-Weyl algebra in commutative space is elucidated. Equivalency conditions between two algebras are clarified. It is explored that the deformed algebra related to the undeformed one by a non-orthogonal similarity transformation. Furthermore, non-exist...

We discuss the rôle of quantum deformation of Weyl-Heisenberg algebra in dissipative systems and finite temperature systems. We express the time evolution generator of the damped harmonic oscillator and the generator of thermal Bogolubov transformations in terms of operators of the quantum Weyl-Heisenberg algebra. The quantum parameter acts as a label for the unitarily inequivalent representati...

Geodesics are studied in one of the Weyl metrics, referred to as the M–Q solution. First, arguments are provided, supporting our belief that this space–time is the more suitable (among the known solutions of the Weyl family) for discussing the properties of strong quasi–spherical gravitational fields. Then, the behaviour of geodesics is compared with the spherically symmetric situation, bringin...

An operator T acting on a Banach space X satisfies the property (UWE) if σa(T ) r σSF− + (T ) = E(T ), where σa(T ) is the aproximate point spectrum of T , σ SF− + (T ) is the upper semi-Weyl spectrum of T and E(T ) is the set of all eigenvalues of T that are isolated in the spectrum σ(T ) of T . In this paper, we introduce and study two new spectral properties, namely (VE) and (VEa ), in conne...

We investigate the theory of the finite Heisenberg-Weyl group in relation to the development of adaptive radar and to the construction of spreading sequences and error-correcting codes in communications. We contend that this group can form the basis for the representation of the radar environment in terms of operators on the space of waveforms. We also demonstrate, following recent developments...

A bstract The double copy relates momentum-space scattering amplitudes in gauge and gravity theories. It has also been extended to classical solutions, where some cases an exact can be formulated directly terms of products fields position space. This is seemingly at odds with the origins copy, question why copies are possible space — when this form will break remained largely unanswered. In pap...

Abstract In the present paper we further study of compression cone a real spherical homogeneous space $$Z=G/H$$ Z = G / H . particular provide geometric construction little Weyl group Z introduced recently by Knop and K...

The discrete symmetries of the Lorentz group are on the one hand a ‘complex’ interplay between linear and anti-linear operations on spinor fields and on the other hand simple linear reflections of the Minkowski space. We define operations for T , CP and CPT leading to both kinds of actions. These operations extend the action of SL(2, CI ), representing the action of the proper orthochronous Lor...

Let n, r be integers 1 and let V be a vector space of dimension n over C. Classically, we have natural commuting actions of the general linear group GL(V) and the symmetric group Sr on the tensor space V⊗r, and both actions satisfy the so-called Weyl reciprocity [W] (or the double centralizer property), which has been used by Schur and Weyl to link representations of Sr with representations of ...