Developments for a Relativistic Many-1/2-Fermion Theory

Eliade N. Stefanescu

Gautam Rupak, Thomas Schäfer

F. Sanchez-Martin, F. Lopez-Gordo

Benjamin Simmen, Edit Mátyus, Markus Reiher

Abstract This paper presents the derivation of a kinetic-balance condition for explicitly correlated basis functions employed in semi-classical relativistic calculations. Such a condition is important to ensure variational stability in algorithms based on the first-quantized Dirac theory of 1/2-fermions. We demonstrate that the kinetic-balance condition can be obtained from the row reduction process commonly applied to solve systems of linear equations. The resulting form of kinetic balance establishes a relation for the components of the spinor of an N -fermion system to the non-relativistic limit, which is in accordance with recent developments in the field of exact decoupling in relativistic orbital-based many-electron theory.

Pieter Kok, Samuel L. Braunstein

We derive the relativistic transformation laws for the annihilation operators of the scalar field, the massive spin-1 vector field, the electromagnetic field and the spinor field. The technique developed here involves straightforward mathematical techniques based on fundamental quantum field theory, and is applicable to the study of entanglement in arbitrary coordinate transformations. In particular, it predicts particle creation for non-inertial motion. Furthermore, we present a unified description of relativistic transformations and multi-particle interferometry with bosons and fermions, which encompasses linear optical quantum computing.

V. E. Rochev