Related papers: The nilpotent Dirac equation and its applications …
We present various generalizations of the Dirac formalism. The different-parity solutions of the Weinberg's 2(2J+1)-component equations are found. On this basis, generalizations of the Bargmann-Wigner (BW) formalism are proposed. Relations…
Some years ago, one of the authors~(MM) revived a concept to which he gave the name of single-particle Dirac oscillator, while another~(CQ) showed that it corresponds to a realization of supersymmetric quantum mechanics. The Dirac…
New features are described for models with multi-particle area-dependent potentials, in any number of dimensions. The corresponding many-body field theories are investigated for classical configurations. Some explicit solutions are given,…
We study Dirac field equations coupled to electrodynamics with metric and torsion fields: we discuss how special spinorial solutions are incompatible with torsion; eventually these results will be used to sketch a discussion on the problem…
We analyse a modified Dirac equation based on a noncommutative structure in phase space. The noncommutative structure induces generalised momenta and contributions to the energy levels of the standard Dirac equation. Using techniques of…
Recently the interest in relativistic quantum plasma is increasing primarily to understand the fundamentals of the plasma behaviour and its properties. Mathematical models used to investigate these plasma are still need to be matured.…
The Dirac equation for an electron in a finite dipole potential has been studied within the method of linear combination of atomic orbitals (LCAO). The Coulomb potential of the nuclei that compose a dipole is regularized, by considering the…
Noticing that the point-form approach referred to in many recent works implies physics described on hyperplanes, an approach inspired from Dirac's one, which involves a hyperboloid surface, is presented. A few features pertinent to this new…
We introduce a new class of nonlocal kinetic equations and nonlocal Fokker-Planck equations associated with an effective generalized thermodynamical formalism. These equations have a rich physical and mathematical structure that can…
A generalization of the standard model of Dirac particle in external electromagnetic field is proposed. In the generalization we take into account interactions of this particle with environment, which is described by the memory function.…
One more mode developed to get eigen energies and states for the one-electron Dirac's equation with spherically symmetric bound potential. For the particular case of the Coulomb potential it was shown that the method is free of so called…
I present a concise review of where we stand in particle physics today. First, I will discuss QCD, then the electroweak sector and finally the motivations and the avenues for new physics beyond the Standard Model.
The extended Cornell potential which the harmonic oscillator potential is included in the original Cornell potential. The Dirac equation is solved by reducing the Dirac equation to the form of Schrodinger equation. The Nikiforov-Uvarov…
Dirac delta function of matrix argument is employed frequently in the development of diverse fields such as Random Matrix Theory, Quantum Information Theory, etc. The purpose of the article is pedagogical, it begins by recalling detailed…
We start to develop the quantization formalism in a hyperbolic Hilbert space. Generalizing Born's probability interpretation, we found that unitary transformations in such a Hilbert space represent a new class of transformations of…
The virial and the Hellmann--Feynman theorems for massless Dirac electrons in a solid are derived and analyzed using generalized continuity equations and scaling transformations. Boundary conditions imposed on the wave function in a finite…
The problem of classical particle in linear potential is studied by using the formalism of Hilbert space and tomographic probability distribution. The Liouville equation for this problem is solved by finding the density matrix satisfying…
The Dirac equation has resided among the greatest successes of modern physics since its emergence as the first quantum mechanical theory fully compatible with special relativity. This compatibility ensures that the expectation value of the…
Studies in nuclear and atomic physics have played an important role in developing our understanding of the Standard Model of electroweak interactions. We review the basic ingredients of the Standard Model, and discuss some key nuclear and…
Quantum dynamics of a Dirac particle in a 1D box with moving wall is studied. Dirac equation with time-dependent boundary condition is mapped onto that with static one, but with time-dependent mass. Exact analytical solution of such…