Summary
It is shown that, in the Dirac theory of a free electron, the Foldy-Wouthuysen transformation corresponds to the Lorentz transformation from the laboratory to the rest system of the electron, together with a factor which preserves the norm of the wave function. This consideration resolves the ambiguity in the Foldy-Wouthuysen transformation. Also it is shown that covariantly-defined Lorentz-tensor operators may be interpreted as Lorentz transforms of matrix operators from the rest to the laboratory system.
Riassunto
Si dimostra che, nella teoria di Dirac dell’elettrone libero, la trasformazione di Foldy-Wouthuysen corrisponde alla trasformazione di Lorentz dal sistema del laboratorio al sistema di riposo dell’elettrone, con un fattore che conserva la norma della funzione d’onda. Questa considerazione risolve l’ambiguità della trasformazione di Foldy-Wouthuysen. Si mostra anche che gli operatori del tensore di Lorentz definito covariantemente possono essere interpretati come trasformate di Lorentz degli operatori di matrice dal sistema di riposo al sistema del laboratorio.
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References
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M. E. Rose andE. H. Good, Jr.:Nuovo Cimento,22, 565 (1961).
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M. E. Rose:Relativistic Electron Theory (New York, 1961), p. 86.
D. M. Fradkin andR. H. Good, Jr.:Nuovo Cimento,22, 643 (1961).
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Partially supported by the U. S. Atomic Energy Commission.
The work of this author was done in the Ames Laboratory of the U. S. Atomic Energy Commission.
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Good, E.H., Rose, M.E. Relation between Foldy-Wouthuysen and lorentz transformations. Nuovo Cim 24, 864–869 (1962). https://doi.org/10.1007/BF02751460
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DOI: https://doi.org/10.1007/BF02751460