Foldy-Wouthuysen transformations in an indefinite-metric space. I. Necessary and sufficient conditions for existence
Journal Article
·
· Phys. Rev., D; (United States)
We prove that the necessary and sufficient conditions that a pseudounitary (Foldy--Wouthuysen) transformation exists which will diagonalize a nondiagonal pseudo-Hermitian matrix O on a (nonsingular) indefinite-metric space are that all the eigenvalues of O be real and all the eigenvectors of O have nonzero norm. Physical applications are discussed. For example, the 2 x 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 Poincare generators to a form which decouples the different mass (and normed) states. (AIP)
- Research Organization:
- Theoretical Division, Los Alamos Scientific Laboratory, University of California, Los Alamos, New Mexico 87545
- OSTI ID:
- 7364959
- Journal Information:
- Phys. Rev., D; (United States), Vol. 13:8; Conference: EDB-644002
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
FOLDY-WOUTHUYSEN TRANSFORM
HERMITIAN MATRIX
EIGENSTATES
EIGENVALUES
LEE MODEL
METRICS
QUANTUM MECHANICS
QUANTUM OPERATORS
CANONICAL TRANSFORMATIONS
MATHEMATICAL MODELS
MATHEMATICAL OPERATORS
MATRICES
MECHANICS
PARTICLE MODELS
657002* - Theoretical & Mathematical Physics- Classical & Quantum Mechanics
GENERAL PHYSICS
FOLDY-WOUTHUYSEN TRANSFORM
HERMITIAN MATRIX
EIGENSTATES
EIGENVALUES
LEE MODEL
METRICS
QUANTUM MECHANICS
QUANTUM OPERATORS
CANONICAL TRANSFORMATIONS
MATHEMATICAL MODELS
MATHEMATICAL OPERATORS
MATRICES
MECHANICS
PARTICLE MODELS
657002* - Theoretical & Mathematical Physics- Classical & Quantum Mechanics