Related papers: Splitting the Kemmer-Duffin-Petiau Equations
Spectroscopic labels for a few particles with spin that are harmonically trapped in one-dimension with effectively zero-range interactions are provided by quantum numbers that characterize the symmetries of the Hamiltonian: permutations of…
We study if there is an opportunity to describe quantum particles in the vicinity of three types of cosmological singularities, big bang-big crunch, big rip and big brake. Writing down the Dirac equation for spinors, and choosing a…
The approximate analytical solutions of the Dirac equations with the reflectionless-type and Rosen-Morse potentials including the spin-orbit centrifugal (pseudo-centrifugal) term are obtained. Under the conditions of spin and pseudospin…
We investigate the set of partial partitions of a finite set, ordered by inclusion. With this ordering the set of partial partitions can be studied as an abstract simplicial complex. We use the theory of shellable nonpure complexes to find…
We propose a generalization of pseudospin and spin symmetries, the SU(2) symmetries of Dirac equation with scalar and vector mean-field potentials originally found independently in the 70's by Smith and Tassie, and Bell and Ruegg. As…
The Klein-Gordon and Dirac equations in a semi-infinite lab ($x > 0$), in the background metric $\ds^2 = u^2(x) (-\dt^2 + \dx^2) + \dy^2 + \dz^2$, are investigated. The resulting equations are studied for the special case $ u(x) = 1 + g x$.…
This paper studies the problem of decomposing a low-rank positive-semidefinite matrix into symmetric factors with binary entries, either $\{\pm 1\}$ or $\{0,1\}$. This research answers fundamental questions about the existence and…
We investigate the quantum mechanical wave equations for free particles of spin 0,1/2,1 in the background of an arbitrary static gravitational field in order to explicitly determine if the phase of the wavefunction is $S/\hbar = \int…
Assuming the canonical seesaw mechanism together with an SO(3) family symmetry for leptons, broken only by the charged-lepton masses, I show that the three neutrinos of Majorana mass $m_0$ are split radiatively in two loops by a maximum…
By assuming that there is no significant intrinsic polarization of the gluon, we have computed the polarized quark contributions to the proton's spin under SU(3) flavor symmetry breaking for the polarized sea and have performed a global…
We present a new procedure of isospin symmetry breaking of cooper-quartets in nuclear matter using Ginzburg-Landau theory, namely we couple the cooper-quartets to the pion-meson field and $SU(2)$ gluons. The paper also describes phenomena…
The generalized Dirac equation of the third order, describing particles with spin 1/2 and three mass states, is analyzed. We obtain the first order generalized Dirac equation in the 24-dimensional matrix form. The mass and spin projection…
In the framework of Lagrangian perturbation theory in general relativity we discuss the possibility to split the Einstein equations, written in terms of spatial Cartan coframes within a 3+1 foliation of spacetime, into gravitoelectric and…
In this paper we proceed into the next step of formalization of a consistent dual theory for mass dimension one spinors. This task is developed approaching the two different and complementary aspects of such duals, clarifying its algebraic…
I present explicit examples of generalizations in relativistic quantum mechanics. First of all, I discuss the generalized spin-1/2 equations for neutrinos. They have been obtained by means of the Gersten-Sakurai method for derivations of…
Various theories of spinning particles are interpreted as realizing elements of an underlying geometric theory. Classical particles are described by trajectories on the Poincare group. Upon quantization an eleven-dimensional Kaluza-Klein…
We compute the weighted enumeration of plane partitions contained in a given box with complementation symmetry where adding one half of an orbit of cubes and removing the other half of the orbit changes the weight by -1 as proposed by…
The rest masses of the stable mesons and baryons and the rest masses of their antiparticles, as well as the rest masses of the mu (+,-) and tau (+,-) leptons can be explained, within 1% accuracy, with the standing wave model, which uses…
By exploiting the freedom in defining the dual of spinors, we report an unexpected theoretical discovery of a quantum field theory of spin-half bosons. It fulfils Dirac's 1969-70 observation that "there must be boson variables connected…
We consider the three-dimensional Dirac equation in spherical coordinates with coupling to static electromagnetic potential. The space components of the potential have angular (non-central) dependence such that the Dirac equation is…