Foldy-Wouthuysen transformations in an indefinite-metric space. I. Necessary and sufficient conditions for existence

Journal Article · Thu Apr 15 04:00:00 EST 1976 · Phys. Rev., D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.13.2245· OSTI ID:7364959

Krajcik, R A; Nieto, M M

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), Journal Name: Phys. Rev., D; (United States) Vol. 13:8; ISSN PRVDA
• Country of Publication: United States
• Language: English

Related Subjects

657002* -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CANONICAL TRANSFORMATIONS
EIGENSTATES
EIGENVALUES
FOLDY-WOUTHUYSEN TRANSFORM
HERMITIAN MATRIX
LEE MODEL
MATHEMATICAL MODELS
MATHEMATICAL OPERATORS
MATRICES
MECHANICS
METRICS
PARTICLE MODELS
QUANTUM MECHANICS
QUANTUM OPERATORS