Foldy-Wouthuysen transformations in an indefinite-metric space. I. Necessary and sufficient conditions for existence
- 15 April 1976
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review D
- Vol. 13 (8), 2245-2249
- https://doi.org/10.1103/physrevd.13.2245
Abstract
We prove that the necessary and sufficient conditions that a pseudounitary (Foldy-Wouthuysen) transformation exists which will diagonalize a nondiagonal pseudo-Hermitian matrix on a (nonsingular) indefinite-metric space are that all the eigenvalues of be real and all the eigenvectors of have nonzero norm. Physical applications are discussed. For example, the 2 × 2 case is discussed in general and for the Sakata-Taketani spin-0 field and the Lee model. This theorem also allows one to show that one can transform all the Bhabha Poincaré generators to a form which decouples the different mass (and normed) states.
Keywords
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