Related papers: Schwinger's non-commutative coordinates and dualit…
The article surveys quantization schemes for metric graphs with spin. Typically quantum graphs are defined with the Laplace or Schrodinger operator which describe particles whose intrinsic angular momentum (spin) is zero. However, in many…
The non-perturbative electron-positron pair production (Schwinger effect) is considered for space- and time-dependent electric fields $\vec{E}(\vec{x},t)$. Based on the Dirac-Heisenberg-Wigner (DHW), formalism we derive a system of partial…
We construct a nonrelativistic wave equation for spinning particles in the noncommutative space (in a sense, a $\theta$-modification of the Pauli equation). To this end, we consider the nonrelativistic limit of the $\theta$-modified Dirac…
We study the theory of the Lorentz group (1/2,0)+(0,1/2) representation in the helicity basis of the corresponding 4-spinors. As Berestetski, Lifshitz and Pitaevskii mentioned, the helicity eigenstates are not the parity eigenstates.…
The (group and spin space) matrix Hamiltonian describing the dynamics of a nonrelativistic spin 1/2 particle moving in a static, but spatially dependent, non-Abelian magnetic field in two spatial dimensions is shown to take the form of an…
We revise the problem of the quantization of relativistic particle models (spinless and spinning), presenting a modified consistent canonical scheme. One of the main point of the modification is related to a principally new realization of…
We construct a nonrelativistic wave equation for spinning particles in the noncommutative space (in a sense, a $\theta$-modification of the Pauli equation). To this end, we consider the nonrelativistic limit of the $\theta$-modified Dirac…
For a bi-partite quantum system defined in a finite dimensional Hilbert space we investigate in what sense entanglement change and interactions imply each other. For this purpose we introduce an entanglement operator, which is then shown to…
The spin-1 Heisenberg model on a triangular lattice with the ferromagnetic nearest- and antiferromagnetic third-nearest-neighbor exchange interactions, $J_1=-(1-p)J$ and $J_2=pJ$, $J>0$ $ (0 \leq p \leq 1)$, is studied with the use of the…
Relativistic dynamics with energy and momentum resricted to an anti-de-Sitter space is presented, specifically in the introduction of coordiate operators conjugate to such momenta. Definition of functions of these operators, their…
The domain of wave functions and effective potentials of the Dirac and Klein-Gordon equations for quantum-mechanical particles in static centrally symmetric gravitational fields are analyzed by taking into account the Hilbert causality…
A modification of the ground state of the classical-spin Heisenberg Hamiltonian in the presence of a weak superstructural distortion of an otherwise Bravais lattice is examined. It is shown that a slight modulation of the crystal lattice…
In a former paper we proposed a model for the quantization of gravity by working in a bundle $E$ where we realized the Hamilton constraint as the Wheeler-DeWitt equation. However, the corresponding operator only acts in the fibers and not…
Our main proposition is that field equations for all spins can be obtained from Casimir eigenvalue equations for Poincare group. We have already confirm that statement for massive scalar, spinor and vector fields in Ref.[1]. In the present…
It is shown that the commonly accepted definition for the Casimir scalar operators of the Poincare group does not satisfy the properties of Casimir invariance when applied to the non-inertial motion of elementary particles while in the…
Position deformation of a Heisenberg algebra and Hilbert space representation of both maximal length and minimal momentum uncertainties may lead to loss of Hermiticity of some operators that generate this algebra. Consequently, the…
In this paper we study a model of the two-dimensional quantum harmonic oscillator in a 3-dimensional anti-de Sitter background. We use a generalized Schr\"odinger picture in which the analogs of the Schr\"odinger operators of the particle…
We investigate the spin dynamics and the conservation of helicity in the first order $S-$matrix of a Dirac particle in any static magnetic field. We express the dynamical quantities using a coordinate system defined by the three mutually…
We prove the split property for any finite helicity free quantum fields. Finite helicity Poincar\'e representations extend to the conformal group and the conformal covariance plays an essential role in the argument. The split property is…
In this work we examine noncommutativity of position coordinates in classical symplectic mechanics and its quantisation. In coordinates $\{q^i,p_k\}$ the canonical symplectic two-form is $\omega_0=dq^i\wedge dp_i$. It is well known in…