Generalized Continuity Equations for Schrödinger and Dirac Equations
Abstract
The concept of the generalized continuity equation (GCE) was recently introduced in [J. Phys. A: Math. and Theor. {\bf 52}, 1552034 (2019)], and was derived in the context of $N$ independent Schrödinger systems. The GCE is induced by a symmetry transformation which mixes the states of these systems, even though the $N$system Lagrangian does not. As the $N$system Schrödinger Lagrangian is not invariant under such a transformation, the GCE will involve source terms which, under certain conditions vanish and lead to conserved currents. These conditions may hold globally or locally in a finite domain, leading to globally or locally conserved currents, respectively. In this work, we extend this idea to the case of arbitrary $SU(N)$transformations and we show that a similar GCE emerges for $N$ systems in the Dirac dynamics framework. The emerging GCEs and the conditions which lead to the attendant conservation laws provide a rich phenomenology and potential use for the preparation and control of fermionic states.
 Publication:

arXiv eprints
 Pub Date:
 February 2021
 arXiv:
 arXiv:2103.00052
 Bibcode:
 2021arXiv210300052K
 Keywords:

 Quantum Physics;
 Mathematical Physics
 EPrint:
 10 pages, 2 figures, 1 table