Zeitschrift für Naturforschung A · 1962 · 126 citations · 0 references
Natural SciencesMathematicsPhysicsElectromagnetismMathematical PhysicsTheoretical PhysicsClassical MechanicsHamiltonian MechanicsLie AlgebrasMaxwell's EquationsQuantum Field TheoryConservation LawsElectromagnetic Field TheoryMomentum Of Electromagnetic FieldsNoether TheoremNoether's Theorem In MechanicsNoether's Theorem In RelativitySpinor Theory
A systematic classification, based on functional criteria, is given for the local conservation laws. Three kinds of conversation laws and current vectors are distinguished. While those of the first and third kind are well-known, those of the second kind are rarely considered. The method of deriving conservation laws due to NOETHER leads to what we call proper current vectors of the first kind, from which all other current vectors of the first kind may be derived by adding some current vector of the third kind. Between the proper current vectors of the first kind and the invariance properties of the Lagrangian there exists a one-one-correlation. The conservation laws of the second kind are not in this way related to invariance properties, but their significance is strongly restricted by a theorem due to FLETCHER. The results obtained are used in an attempt to shed some light on the problem of the electromagnetic field in the HEISENBERG non-linear spinor theory.