Faculty of Mathematics, Physics
and Informatics
Comenius University Bratislava

Seminar of Theoretical Physics - Stanislav Komorovský (21.3.2017)

Tuesday 21.3.2017 at 14:00, Lecture room F2/125

03. 03. 2017 21.15 hod.
By: Peter Maták

Stanislav Komorovský:
New quantum number for the many-electron Dirac-Coulomb Hamiltonian

By breaking the spin symmetry in the relativistic domain, a powerful tool in physical sciences was lost. In this presentation, we will examine an alternative of spin symmetry for systems described by the many-electron Dirac-Coulomb Hamiltonian. We will show that the square of many-electron operator $K_+$, defined as a sum of individual single-electron time-reversal (TR) operators, is a linear Hermitian operator which commutes with the Dirac-Coulomb Hamiltonian in a finite Fock subspace. In contrast to the square of a standard unitary many-electron TR operator $K$, the $K^2_+$ has a rich eigenspectrum having potential to substitute spin symmetry in the relativistic domain. We will demonstrate that $K_+$ is connected to $K$ through an exponential mapping, in the same way as spin operators are mapped to the spin rotational group. Consequently, we call $K_+$ the generator of the many-electron TR symmetry. A new quantum number associated with $K^2_+$ has potential to be used in many areas, for instance, (a) to design effective spin Hamiltonians for electron spin resonance spectroscopy of heavy-element containing systems; (b) to increase efficiency of methods for the solution of many-electron problems in relativistic computational chemistry and physics; (c) to define Kramers contamination in unrestricted density functional and Hartree-Fock theory as a relativistic analog of the spin contamination in the nonrelativistic domain.