Related papers: Pseudoclassical supersymmetrical model for 2+1 Dir…
A pseudoclassical theory of Weyl particle in the space--time dimensions $D=2n$ is constructed. The canonical quantization of that pseudoclassical theory is carried out and it results in the theory of the $D=2n$ dimensional Weyl particle in…
I shortly describe semi-classical models of spinning electron and list a number of theoretical issues where these models turn out to be useful, see arXiv:1710.07135 for details. Then I discuss the possibility to extend the range of…
The behavior of spin doublets is known to play a major role in nuclear structure and shell effects. Pseudo-spin doublets are also known to impact the single-particle spectrum. The covariant framework, having these two effects encoded in its…
Using 2 more time variables as the quantum hidden variables, we derive the equation of Dirac field under the principle of classical physics, then we extend our method into the quantum fields with arbitrary spin number. The spin of particle…
We study $(1+1)$ dimensional Dirac equation with non Hermitian interactions, but real energies. In particular, we analyze the pseudoscalar and scalar interactions in detail, illustrating our observations with some examples. We also show…
This work takes place over a conformally flat spin manifold (M,g). We prove existence and uniqueness of the conformally equivariant quantization valued in spinor differential operators, and provide an explicit formula for it when restricted…
We discuss the possible applications supersymmetric theories might find in the field of elementary particle physics. The supersymmetric generalization of the $SU(3)\times SU(2)\times U(1)$ standard model is discussed in detail. Special…
The classical and quantum model of high spin particles with spin-mass coupling is presented in this paper. The mass spectrum of the model is symmetric with respect to particle-antiparticle exchange. The quantum model contains elementary…
A recent development of the studies on classical and quasi-classical properties of supersymmetric quantum mechanics in Witten's version is reviewed. First, classical mechanics of a supersymmetric system is considered. Solutions of the…
The `classical' model for a massive spinning particle, which was recently proposed, is derived from the isotropic rotator model. Through this derivation, we note that the spin can be understood as the relativistic extension of the isotropic…
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…
We propose a new variant of the semiclassical quantisation with two independent parameters. The first one is proportional to the Planck constant as usually and the second one is connected with a deviation of the given potential from a very…
The quantum-to-classical correspondence (QCC) in spin models is a puzzling phenomenon where the static susceptibility of a quantum system agrees with its classical-system counterpart, at a different corresponding temperature, within the…
It has been found that quantum corrections can substantially affect the classical results of tracking for trajectories close to the separatrix. Hence the development of a basic formalism for obtaining the quantum maps for any particle beam…
Quaternionic and octonionic spinors are introduced and their fundamental properties (such as the space-times supporting them) are reviewed. The conditions for the existence of their associated Dirac equations are analyzed. Quaternionic and…
The distinct models that describe spin 1 and 2 massive excitations in 2+1 dimensions are analized, showing their equivalence (between models of same spin) and analogies (between models of different spin). Topics as spontaneous symmetry…
The Dirac equation is solved for a pseudoscalar Coulomb potential in a two-dimensional world. An infinite sequence of bounded solutions are obtained. These results are in sharp contrast with those ones obtained in 3+1 dimensions where no…
The pseudospin symmetry is a relativistic dynamical symmetry connected with the small component of the Dirac spinor. The origin of pseudospin symmetry in single particle bound states in atomic nuclei has been revealed and studied…
The Standard Model may be included within a supersymmetric theory, postulating new sparticles that differ by half-a-unit of spin from their standard model partners, and by a new quantum number called R-parity. The lightest one, usually a…
The 2(2s+1)-component relativistic basis spinors for the arbitrary spin particles are established in position, momentum and four-dimensional spaces, where s=0,1 / 2,1, 3 / 2, 2, ... . These spinors for integral- and half-integral spins are…