Related papers: On the quantization and generalized uncertainty re…
Quantum Mechanics at Planck scale is considered as a deformation of the conventional Quantum Mechanics. Similar to the earlier works of the author, the main object of deformation is the density matrix. On this basis a notion of the entropy…
A general theory of preparational uncertainty relations for a quantum particle in one spatial dimension is developed. We derive conditions which determine whether a given smooth function of the particle's variances and its covariance is…
We study an algebraic deformation problem which captures the data of the general deformation problem for a quantum vertex algebra. We derive a system of coupled equations which is the counterpart of the Maurer-Cartan equation on the usual…
The author investigates the general Lie algebra of operators of coordinates, momenta, and Lorentz group generators, which can be used in quantum gravity, theories with generalized uncertainty principle, double and triple relativity and…
Uncertainty principle is one of the cornerstones of quantum theory. In the literature, there are two types of uncertainty relations, the operator form concerning the variances of physical observables and the entropy form related to entropic…
We study the implications of a change of coordinatization of momentum space for theories with curved momentum space. We of course find that after a passive diffeomorphism the theory yields the same physical predictions, as one would expect…
Foundations of the formal series $*$ -- calculus in deformation quantisation are discussed. Several classes of continuous linear functionals over algebras applied in classical and quantum physics are introduced. The notion of nonnegativity…
In this work, we present straightforward and concrete computations of the unitary irreducible representations of the Euclidean motion group $M(2)$ employing the methods of deformation quantization. Deformation quantization is a quantization…
The dispersion relation for planar N=4 supersymmetric Yang-Mills is identified with the Casimir of a quantum deformed two-dimensional kinematical symmetry, E_q(1,1). The quantum deformed symmetry algebra is generated by the momentum, energy…
In these notes, we introduce formal hom-associative deformations of the quantum planes and the universal enveloping algebras of the two-dimensional non-abelian Lie algebras. We then show that these deformations induce formal hom-Lie…
A good hundred years after the necessity for a quantum theory of gravity was acknowledged by Albert Einstein, the search for it continues to be an ongoing endeavour. Nevertheless, the field still evolves rapidly as manifested by the recent…
We derive generalised uncertainty relations (GURs) for angular momentum and spin in the smeared-space model of quantum geometry. The model implements a minimum length and a minimum linear momentum, and recovers both the generalised…
We suggest commutation relations for a quantum measure. In one version of these relations, the right-hand side takes account of the presence of curvature of space; in the simplest case, this yields the action of general relativity. We…
In this paper, the generic uncertainty relation (UR) for kernel-based transformations (KT) of signals is derived. Instead of using the statistics approach as shown in the literature before, here we employ quantum mechanical operator…
A generalized Cauchy-Schwarz inequality is derived and applied to uncertainty relation in quantum mechanics. We see a modification in the uncertainty relation and minimum uncertainty wave packet.
A motivation of using noncommutative and nonarchimedean geometry on very short distances is given. Besides some mathematical preliminaries, we give a short introduction in adelic quantum mechanics. We also recall to basic ideas and tools…
The groupoid approach to noncommutative unification of general relativity with quantum mechanics is compared with the canonical gravity quantization. It is shown that by restricting the corresponding noncommutative algebra to its…
Some fundamental aspects related with the construction of Robertson-Schr\"odinger like uncertainty principle inequalities are reported in order to provide an overall description of quantumness, separability and nonlocality of quantum…
The new uncertainty relation is derived in the context of the canonical quantum theory with gravity for the case of the maximally symmetric space. This relation establishes a connection between fluctuations of the quantities which determine…
It is shown that q-deformed quantum mechanics (systems with q-deformed Heisenberg commutation relations) can be interpreted as an ordinary quantum mechanics on Kaehler manifolds, or as a quantum theory with second (or first)- class…