We calculate all symmetries of the Dirac-Pauli equation in twodimensional and three-dimensional Euclidean space. Further, we use our results for an investigation of the issue of zero mode degeneracy. We construct explicitly a class of multiple zero modes with their gauge potentials. email: [email protected] email: [email protected]

We present a weak-relativistic limit comparison between the Kohn-Sham-Dirac equation and its approximate form containing the exchange coupling, which is used in almost all relativistic codes of density-functional theory. For these two descriptions, an exact expression of the Dirac Green’s function in terms of the nonrelativistic Green’s function is first derived and then used to calculate the e...

The Wheeler-DeWitt equation for the Bianchi Class A cosmological models is expressed generally in terms of the second-order differential equation like the Klein-Gordon equation. To obtain the positive-definite probability density, a new method extending the Dirac-Square-Root formalism, which factorizes the Wheeler-DeWitt equation into the first-order differential equation using the Pauli matric...

The Wheeler-DeWitt equation in the Bianchi Class A cosmological models is expressed generally in terms of a second-order differential equation, like the Klein-Gordon equation. To obtain a positive definite probability density, a new method is investigated, which extends the Dirac Square Root formalism that factorizes the Wheeler-DeWitt equation into a first-order differential equation using the...

In this paper, we suggest an alternative strategy to derive the complex two-component Majorana equation with a mass term and elucidate the related Lorentz transformation. The Majorana equation is established completely on its own, rather than derived from the chiral Dirac equation. Thereby, use is made of the complex conjugation operator and Pauli spin matrices only. The eigenfunctions of the t...

We calculate all symmetries of the Dirac-Pauli equation in twodimensional and three-dimensional Euclidean space. Further, we use our results for an investigation of the issue of zero mode degeneracy. We construct explicitly a class of multiple zero modes with their gauge potentials. email: [email protected] email: [email protected]

In this paper, we define energy-momentum density as a product of the complex vector electromagnetic field and its complex conjugate. We derive an equation for the spacetime derivative of the energy-momentum density. We show that the scalar and vector parts of this equation are the differential conservation laws for energy and momentum, and the imaginary vector part is a relation for the curl of...

Recent results on zero modes of the Abelian Dirac operator in three dimensions support to some degree the conjecture that the Chern–Simons action admits only certain quantized values for gauge fields that lead to zero modes of the corresponding Dirac operator. Here we show that this conjecture is wrong by constructing an explicit counterexample. )email address: [email protected] )email addr...

Quantum spin-flip transitions are of great importance in the synchrotron radiation (SR) theory. For better understanding of the nature of this phenomenon, it is necessary to except the effects connected with the electric charge radiation from observation. This fact explains the suggested choice of the spin-flip radiation model in the form of radiation of the electric neutral Dirac-Pauli particl...

We summarise applications of Dyson-Schwinger equations to the theory and phenomenology of hadrons. Some exact results for pseudoscalar mesons are highlighted with details relating to the U A (1) problem. We describe inferences from the gap equation relating to the radius of convergence for expansions of observables in the current-quark mass. We recapitulate upon studies of nucleon electromagnet...