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Lorentz Covariant Wave Functions and Equations for Elementary Systems
Author(s) -
Fonda Luciano,
Ghirardi Gian Carlo
Publication year - 1969
Publication title -
fortschritte der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.469
H-Index - 71
eISSN - 1521-3978
pISSN - 0015-8208
DOI - 10.1002/prop.19690171102
Subject(s) - covariant transformation , representation theory of the lorentz group , irreducible representation , invariant (physics) , poincaré group , lorentz transformation , lorentz group , mathematical physics , wave function , group (periodic table) , pure mathematics , massless particle , mathematics , wave equation , algebra over a field , relativistic wave equations , physics , dirac equation , classical mechanics , mathematical analysis , quantum mechanics , fundamental representation , lie algebra , weight
We give in this paper a detailed and unified description of the procedures which must be followed for all cases of physical interest to go from the wave functions carrying an irreducible representation of the restricted Poincaré group, to objects having a manifestly covariant behaviour. As well known, for instance for the case of spin 1/2 massive particles, this amounts to performing the inverse of a Foldy‐Wouthuysen transformation. Before coming to the main subject of the paper, the construction of the irreducible representations of the restricted and extended Poincaré group are reviewed. Particular emphasis is given to the physical meaning of the representations and of the invariants which characterize them. After this, we derive manifestly covariant quantities from the wave functions of the irreducible representations of the restricted group for spin 0. 1/2 and 1, massive and massless elementary systems. The corresponding relativistically invariant equations, i.e. the Klein‐Gordon, Dirac, Proca, Weyl and Maxwell equations are then derived. The transformations properties under the transformations of the extended group are also extensively discussed.