Related papers: Position-dependent noncommutativity in quantum mec…
The commutation relations for bosons are field independent, and can be reliably inferred from the definition of creation and annihilation operators. Here, the commutation relations are assumed known, and the quantum electrodynamics…
We revisit Wigner's question about the admissible commutation relations for coordinate and velocity operators given their equations of motion (EOM). In more general terms we want to consider the question of how to quantize dynamically…
A deformation of Heisenberg algebra induces among other consequences a loss of Hermiticity of some operators that generate this algebra. Therefore, these operators are not Hermitian, nor is the Hamiltonian operator built from them. In the…
Stabilization, by deformation, of the Poincar\'{e}-Heisenberg algebra requires both the introduction of a fundamental lentgh and the noncommutativity of translations which is associated to the gravitational field. The noncommutative…
A quantum theory of noncommutative fields was recently proposed by Carmona, Cortez, Gamboa and Mendez (hep-th/0301248). The implications of the noncommutativity of the fields, intended as the requirements…
Any effort to localise an event in the vicinity of the Planck length scale, only where the quantum gravitational effects are predicted to be observed, will invariably result in gravitational collapse. One must postulate noncommutative (NC)…
This work introduces a novel $q$-$\hbar$ deformation of the Heisenberg algebra, designed to unify and extend several existing $q$-deformed formulations. Starting from the canonical Heisenberg algebra defined by the commutation relation…
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…
The noncommutativity concept has wide range of applications in physical and mathematical theories. Noncommutativity in the position-time coordinates concerns the microscale structure of space-time. the noncommutativity is an intrinsic…
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…
Second order supersymmetric approach is taken to the system describing motion of a quantum particle in a potential endowed with position-dependent effective mass. It is shown that the intertwining relations between second order partner…
A great number of problems of relativistic position in quantum mechanics are due to the use of coordinates which are not inherent objects of spacetime, cause unnecessary complications and can lead to misconceptions. We apply a…
A demonstration is given that the simplest model of quantum mechanics formulated on a plane non-commutative geometry endowed with a Galilean symmetry group in which the position and linear momentum-variable commutators are first order in…
It seems that the problem of finding a suitable position operator for photon has been solved in a recently published work which is based on a new commutation relation between position and momentum operators of massless particles[1].…
This paper considers a generalization of the notion of quantum observables in ontological models of quantum mechanics. Within this framework it is possible to construct physical models where quantum noncommutativity can arise dynamically.…
Quantum field theories on noncommutative Minkowski space are studied in a model-independent setting by treating the noncommutativity as a deformation of quantum field theories on commutative space. Starting from an arbitrary Wightman…
Recently, some problems have been found in the definition of the partial derivative in the case of the presence of both explicit and implicit functional dependencies in the classical analysis. In this talk we investigate the influence of…
We tested in the framework of quantum mechanics the consequences of a noncommutative (NC from now on) coordinates. We restricted ourselves to 3D rotationally invariant NC configuration spaces with dynamics specified by the Hamiltonian H =…
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…
A structural similarity between Classical Mechanics (CM) and Quantum Mechanics (QM) was revealed by P.A.M. Dirac in terms of Lie Algebras: while in CM the dynamics is determined by the Lie algebra of Poisson brackets on the manifold of…