The supersymmetry of the electron in both the nonstationary magnetic and electric fields in a two-dimensional case is studied. The supercharges which are the integrals of motion and their algebra are established. Using the obtained algebra the solutions of nonstationary Pauli equation are generated. PACS number(s): 03.65.-w; 11.30.Pb

We show how to transform a Dirac equation in a curved static spacetime into a Dirac equation in flat spacetime. In particular, we show that any solution of the free massless Dirac equation in a 1 + 1 dimensional flat spacetime can be transformed via a local phase transformation into a solution of the corresponding Dirac equation in a curved static background, where the spacetime metric is encod...

We study the asymptotic behavior, as Planck’s constant ~ → 0, of the number of discrete eigenvalues and the Riesz means of Pauli and Dirac operators with a magnetic field μB(x) and an electric field. The magnetic field strength μ is allowed to tend to infinity as ~ → 0. Two main types of results are established: in the first μ~ ≤ constant as ~ → 0, with magnetic fields of arbitrary direction; t...

We suggest an alternative mathematical model for the electron in which the dynamical variables are a coframe (field of orthonormal bases) and a density. The electron mass and external electromagnetic field are incorporated into our model by means of a Kaluza–Klein extension. Our Lagrangian density is proportional to axial torsion squared. The advantage of our approach is that it does not requir...

For differential operators which are invariant under the action of an abelian group Bloch theory is the preferred tool to analyze spectral properties. By shedding some new non-commutative light on this we motivate the introduction of a non-commutative Bloch theory for elliptic operators on Hilbert C-modules. It relates properties of C-algebras to spectral properties of module operators such as ...

First-order relativistic corrections to the energy of closed-shell molecular systems are calculated, using all terms in the two-component Breit-Pauli Hamiltonian. In particular, we present the first implementation of the two-electron Breit orbit-orbit integrals, thus completing the first-order relativistic corrections within the two-component Pauli approximation. Calculations of these correctio...

Leading order semi-classical asymptotics are given for the distribution of the eigen-values of Dirac and Pauli operators describing an electron in an electromagnetic eld. Minimal conditions are assumed on the electric and magnetic potentials to ensure the existence of only a nite number of eigenvalues outside the essential spectra. The method used is based on coherent state analysis.

We consider the problem of nding rigorous results for the dynamics of a classical charged point particle interacting with the electromagnetic eld, as described by the standard Maxwell{Lorentz equations. Some results are given for the corresponding linearized system, i.e. the so called dipole approximation, in the presence of a mechanical linear restoring force. We regularize the system by takin...