• Corpus ID: 232076545

Generalized Continuity Equations for Schr\"odinger and Dirac Equations

@inproceedings{Katsaris2021GeneralizedCE,
  title={Generalized Continuity Equations for Schr\"odinger and Dirac Equations},
  author={Angelos Katsaris and Panayotis A. Kalozoumis and Fotis K. Diakonos},
  year={2021}
}

• A. Katsaris, P. Kalozoumis, F. Diakonos
• Published 26 February 2021
• Mathematics

The concept of the generalized continuity equation (GCE) was recently introduced in [J. Phys. A: Math. and Theor. 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.