Related papers: Uniqueness of conserved currents in quantum mechan…
The quantum theory of relativistic particles, based on the first quantization technique similar to that used by Schroedinger and Dirac in formulating quantum mechanics, is reconsidered on the basis of a photon-like dispersion relation…
Proofs of two statements are provided in this paper. First, the authors prove that the formalism of the pseudo-Hermitian quantum mechanics allows describing the Dirac particles motion in arbitrary stationary gravitational fields. Second, it…
Persistent currents and magnetization are considered for a two-dimensional electron (or gas of electrons) coupled to various magnetic fields. Thermodynamic formulae for the magnetization and the persistent current are established and the…
It is well known that the Klein-Gordon equation in curved spacetime is conformally noninvariant, both with and without a mass term. We show that such a noninvariance provides nontrivial physical insights at different levels, first within…
We exhibit a purely quantum mechanical carrier of the imprints of gravitation by identifying for a relativistic system a property which (i) is independent of its mass and (ii) expresses the Poincare invariance of spacetime in the absence of…
The formalism of quantum mechanics is presented in a way that its interpretation as a classical field theory is emphasized. Two coupled real fields are defined with given equations of motion. Densities and currents associated to the fields…
As currently understood since its discovery, the bare Klein-Gordon theory consists of negative quantum probabilities which are considered to be physically meaningless if not outright obsolete. Despite this annoying setback, these negative…
We construct quantum operators solving the quantum versions of the Sturm-Liouville equation and the resolvent equation, and show the existence of conserved currents. The construction depends on the following input data: the basic quantum…
We analyze the Schr\"{o}dinger dynamics and the Schr\"{o}dinger function (or the so-called wavefunction) in the following four aspects. (1) The Schr\"{o}dinger equation is reconstructed from scratch in the real field only, without referring…
It was pointed out in a previous paper that although neither the Klein-Gordon equation nor the Dirac Hamiltonian produces sound solitary free-particle relativistic quantum mechanics, the natural square-root relativistic Hamiltonian for a…
Kirkwood-Dirac representations of quantum states are increasingly finding use in many areas within quantum theory. Usually, representations of this sort are only applied to provide a representation of quantum states (as complex functions…
A mechanical covariant equation is introduced which retains all the effectingness of the Lagrange equation while being able to describe in a unified way other phenomena including friction, non-holonomic constraints and energy radiation…
We extend the Landauer-B\"uttiker formalism in order to accommodate both unitary and self-adjoint operators which are not bounded from below. We also prove that the pure point and singular continuous subspaces of the decoupled Hamiltonian…
We show, in the case of a special dipolar source, that electromagnetic fields in fractional quantum mechanics have an unexpected space dependence: propagating fields may have non-transverse components, and the distinction between near-field…
We develop a new concept of quantum mechanics which is based on a generalized space-time and on an action vector space similar to it. Both spaces are provided by algebraic properties. This allows to calculate the Dirac matrixes and to…
Gauge invariance is one of the more important concepts in physics. We discuss this concept in connection with the unitary evolution of discrete-time quantum walks in one and two spatial dimensions, when they include the interaction with…
A computational method is proposed to calculate bound and resonant states by solving the Klein-Gordon and Dirac equations for real and complex energies, respectively. The method is an extension of a non-relativistic one, where the potential…
A constraint correlation dynamics up to 4-point Green functions is proposed for SU(N) gauge theories which reduces the N-body quantum field problem to the two-body level. The resulting set of nonlinear coupled equations fulfills all…
The formation of persistent charge currents in mesoscopic systems remains an interesting and actual topic of condensed matter research. Here, we analyze the formation of spontaneous arising persistent currents of charged fermions in…
The symmetry studies of Maxwell equations gave new insight on the nature of electromagnetic (EM) field. It has in general case quaternion single structure, consisting of four independent field constituents, which differ with each other by…