Related papers: Levinson theorem for Dirac particles in two dimens…
A generalized formulation of non-relativistic quantum mechanics is developed within multidimensional geometric (NG) frameworks characterized by a power-law dispersion relation \(E \propto |p|^{j}\), where \(j = N - 1\). Starting from the…
We present a relativistic formulation of noncommutative mechanics were the object of noncommutativity $\theta^{\mu\nu}$ is considered as an independent quantity. Its canonical conjugate momentum is also introduced, what permits to obtain an…
The purpose of the present note is to propose, in the framework of relativistic quantum mechanics, a new Poincare-invariant equation for two particles with masses m_1, m_2 and spin s_1=s_2=1/2. It is a first-order linear differential…
It is shown that a nonrelativistic mechanical system involving a general nonrelativistic potential V(|r1-r2|) between point particles at positions r1 and r2 can be extended to a Lagrangian system which is invariant under Lorentz…
The rotating frame is considered in quantum mechanics on the basis of the position dependent boost relating this frame to the non rotating inertial frame. We derive the Sagnac phase shift and the spin coupling with the rotation in the non…
In a generalized Heisenberg/Schroedinger picture we use an invariant space-time transformation to describe the motion of a relativistic particle. We discuss the relation with the relativistic mechanics and find that the propagation of the…
We report on recent developments towards a relativistic quantum mechanical theory of motion for a fixed, finite number of electrons, photons, and their anti-particles, as well as its possible generalizations to other particles and…
We construct a Hamiltonian for a quantum-mechanical model of nonrelativistic particles in three dimensions interacting via the creation and annihilation of a second type of nonrelativistic particles, which are bosons. The interaction…
Relativistic quantum theory shows that the known Einstein time dilation (ED) approximately holds for the decay law of the unstable particle having definite momentum p (DP). I use a different definition of the moving particle as the state…
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…
In this paper, we study the relativistic quantum problem of a particle constrained to a double cone surface. For this purpose, we build the Dirac equation in a curved space using the tetrads formalism. Two cases are analysed. First, we…
The relativistic two body problem is considered in terms of the action integral in the case of two interacting spinless particles and spin-$1/2$ fermions, interacting by means of vector and scalar fields. The Lagrangians governing the…
Using a generalized procedure for obtaining the equation of motion of a propagating fermionic particle, we examine previous claims for a lightlike preferred axis embedded in the framework of Lorentz-invariance violation with preserved…
By using Meng's idea in his generalization of the classical MICZ-Kepler problem, we obtained the equations of motion of a charged particle in the field of generalized Dirac monopole in odd dimensional Euclidean spaces. The main result is…
The quantum predictions for a single nonrelativistic spin-1/2 particle can be reproduced by noncontextual hidden variables. Here we show that quantum contextuality for a relativistic electron moving in a Coulomb potential naturally emerges…
The observational basis of quantum theory in accelerated systems is studied. The extension of Lorentz invariance to accelerated systems via the hypothesis of locality is discussed and the limitations of this hypothesis are pointed out. The…
The properties of the equation of Dirac type in three-dimensional and five-dimensional Minkowski space-time with respect to time reflection (in sense of Pauli and Wigner) as well as to the operation of charge conjugation are investigated.…
There are constructed exact solutions of the quantum-mechanical Dirac equation for a spin S=1/2 particle in Riemannian space of constant negative curvature, hyperbolic Lobachevsky space, in presence of an external magnetic field, analogue…
We consider infinite random casual Lorentzian triangulations emerging in quantum gravity for critical values of parameters. With each vertex of the triangulation we associate a Hilbert space representing a bosonic particle moving in…
Using the example of a Dirac particle in external static fields, Dirac theory is reformulated as a one-particle quantum theory in the space of normalized two-component spinors. In this formulation, the Dirac operator ``splits'' into two…