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Uniqueness of conserved currents in quantum mechanics
Author(s) -
Holland P.
Publication year - 2003
Publication title -
annalen der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.009
H-Index - 68
eISSN - 1521-3889
pISSN - 0003-3804
DOI - 10.1002/andp.200310022
Subject(s) - uniqueness , physics , classical mechanics , quantum , supersymmetric quantum mechanics , quantum mechanics , mechanics , quantum statistical mechanics , mathematics , mathematical analysis
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 Schrödinger 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.