Summary
The equations and the generators of Wigner's canonical realization of the [m, 1/2] representation of the Poincaré group are obtained in a Lagrangian framework. This is accomplished in configuration space by defining a Lagrangian density onJ 1(J r(E)) (r→∞), whereJ r (E) is the bundle of ther-jets of the Dirac vector bundleE. The expression of the charges associated with the Poincaré generators is then obtained by means of an appropriate extension of the Noether theorem and the origin of a «mean spin» symmetry of the Dirac theory is briefly discussed.
Riassunto
Si ottengono in un sistema Lagrangiano le equazioni e i generatori della realizzazione canonica di Wigner della rappresentazione [m, 1/2] del gruppo di Poincaré. Si fa ciò in uno spazio delle configurazioni definendo una densità lagrangiana suJ 1(J r(E)) (r→∞), doveJ r (E) è il fascio di jetr del fascio vettoriale di DiracE. Si ottiene quindi l'espressione delle cariche associate con i generatori di Poincaré mediante un'estensione appropriata del teorema di Noether e si discute brevemente l'origine di una simmetria a «spin medio» della teoria di Dirac.
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Aldaya, V., de Azcárraga, J.A. Fibre bundles and canonical representations of the Poincaré group (classm≠0) in a Lagrangian formalism. Nuov Cim A 49, 137–150 (1979). https://doi.org/10.1007/BF02896718
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DOI: https://doi.org/10.1007/BF02896718