We study the energy of relativistic electrons and positrons interacting via the second quantized Coulomb potential in the field of a nucleus of charge Z within the Hartree-Fock approximation. We show that the associated functional has a minimizer. In addition, all minimizers are purely electronic states, they are projections, and fulfill the no-pair Dirac-Fock equations.

Effects of the relativistic correction Coulomb interaction on doubly-magic nuclei are discussed with Skyrme Hartree--Fock calculations. The is treated by using local density approximation. It found that to total energy about $ 2.4 \, \mathrm{MeV} for {}^{208} \mathrm{Pb} $, while proton and neutron radii do not change significantly. This difference larger than exchange (Fock) calculated (Hartre...

We write the fermionic q-Fock space representation of Uq(ŝln) as an infinite extended braided tensor product of finite-dimensional fermionic Uq(sln)-quantum planes or exterior algebras. Using braided geometrical techniques developed for such quantum exterior algebras, we provide a new approach to the Kashiwara-Miwa-Stern action of the Heisenberg algebra on the q-fermionic Fock space, obtaining ...

We continue the investigation of the Lévy processes on a q-deformed full Fock space started in [1]. First, we show that the vacuum vector is cyclic and separating for the algebra generated by such a process. Next, we describe a chaotic representation property for it in terms of multiple integrals with respect to diagonal measures, in the style of Nualart and Schoutens. We define stochas-tic int...

Charge-density distributions and the associated nuclear radii are calculated with the Hartree-Fock method for comparison with available data from electron scattering. Two forms of Skyrme interactions are used for the calculations. As a further refinement the single-particle occupancies are constrained to values obtained from shell-model calculations. A significant improvement in the agreement i...

A two-parameter deformed superoscillator system with SUq1/q2(n | m)-covariance is presented and used to construct a two-parameter deformed N = 2 SUSY algebra. The Fock space representation of the algebra is discussed and the deformed Hamiltonian for such generalized superoscillators is obtained.

We prove that in the Euclidean representation of the three dimensional massless Nelson model the t = 0 projection of the interacting measure is absolutely continuous with respect to a Gaussian measure with suitably adjusted mean. We also determine the Hamiltonian in the Fock space over this Gaussian measure space.

We report on the first Skyrme-Hartree-Fock calculations with the tilted-axis cranking in the context of magnetic rotation. The mean field symmetries , differences between phenomenological and self-consistent methods and the generation of shears-like structures in the mean field are discussed. Significant role of the time-odd spin-spin effective interaction is pointed out. We reproduce the shear...

All possible Bogoliubov operators that generate the thermal transformations in Thermo Field Dynamics (TFD) form a SU (1, 1) group. We discuss this construction in the bosonic string theory. In particular, the transformation of the Fock space and string operators generated by the most general SU(1, 1) unitary Bogoliubov transformation and the entropy of the corresponding thermal string are compu...