Uniqueness of conserved currents in quantum mechanics

Details Uniqueness of conserved currents in quantum mechanics Uniqueness of conserved currents in quantum mechanics

2003-05-29

arxiv.org/abs/quant-ph/0305175v1

Ann. Phys. (Leipzig) 12, 446-62 (2003) (slightly modified version)

Physics

Quantum Physics

22 pages

Scientific paper

10.1002/andp.200310022

It is proved by a functional method that the conventional expression for the Dirac current is the only conserved 4-vector implied by the Dirac equation that is a function of just the quantum state. The demonstration is extended to derive the unique conserved currents implied by the coupled Maxwell-Dirac equations and the Klein-Gordon equation. The uniqueness of the usual Pauli and Schrodinger currents follows by regarding these as the non-relativistic limits of the Dirac and Klein-Gordon currents, respectively. The existence and properties of further conserved vectors that are not functions of just the state is examined.

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