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Uncertainties in the Foldy-Wouthuysen transformation

Technical Report:

Abstract

The Foldy-Wouthuysen (W-F) transformation is designed to transform the Hamiltonian of a fermion to a block diagonalized one in order to make the physical contents explicit. At the limit of zero interaction, this diagonalization can be done completely. With interactions. the diagonalization is incomplete and can be done only in the nonrelativistic limit to the extent of neglecting higher orders of 1/m where m is the mass of the fermion. Although the F-W transformations are not uniquely defined in either case, the ambiguity in the final results appears only in the case of incomplete diagonalization. For some very special interactions, this ambiguity has been studied, however, this article will show that the ambiguity exists in general. Therefore, care must be taken when displaying the physical contents of an interacting Hamiltonian by F-W transformation. Extra information must be invoked to guarantee the unique and correct result.
Authors:
Publication Date:
Aug 01, 1991
Product Type:
Technical Report
Report Number:
UM-P-91/61; SSCL-499.
Reference Number:
SCA: 662100; PA: AIX-24:003279; SN: 93000913729
Resource Relation:
Other Information: PBD: Aug 1991
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; FERMIONS; FOLDY-WOUTHUYSEN TRANSFORM; DIRAC EQUATION; HAMILTONIANS; QUANTUM ELECTRODYNAMICS; 662100; GENERAL THEORY OF PARTICLES AND FIELDS
OSTI ID:
10109015
Research Organizations:
Melbourne Univ., Parkville, VIC (Australia). School of Physics
Country of Origin:
Australia
Language:
English
Other Identifying Numbers:
Other: ON: DE93609879; TRN: AU9212913003279
Availability:
OSTI; NTIS (US Sales Only); INIS
Submitting Site:
INIS
Size:
[7] p.
Announcement Date:
Jun 30, 2005

Technical Report:

Citation Formats

Wu, Dandi. Uncertainties in the Foldy-Wouthuysen transformation. Australia: N. p., 1991. Web.
Wu, Dandi. Uncertainties in the Foldy-Wouthuysen transformation. Australia.
Wu, Dandi. 1991. "Uncertainties in the Foldy-Wouthuysen transformation." Australia.
@misc{etde_10109015,
title = {Uncertainties in the Foldy-Wouthuysen transformation}
author = {Wu, Dandi}
abstractNote = {The Foldy-Wouthuysen (W-F) transformation is designed to transform the Hamiltonian of a fermion to a block diagonalized one in order to make the physical contents explicit. At the limit of zero interaction, this diagonalization can be done completely. With interactions. the diagonalization is incomplete and can be done only in the nonrelativistic limit to the extent of neglecting higher orders of 1/m where m is the mass of the fermion. Although the F-W transformations are not uniquely defined in either case, the ambiguity in the final results appears only in the case of incomplete diagonalization. For some very special interactions, this ambiguity has been studied, however, this article will show that the ambiguity exists in general. Therefore, care must be taken when displaying the physical contents of an interacting Hamiltonian by F-W transformation. Extra information must be invoked to guarantee the unique and correct result.}
place = {Australia}
year = {1991}
month = {Aug}
}