An Integral Transform in de Sitter Space

Research output: Contribution to journalArticle

Abstract

An integral transform on (4 + 1) de Sitter space, which is a generalization of the Fourier transform for a Dirac particle in Minkowski space, is considered, and proofs of its relevant properties are provided. With this integral transform we demonstrate explicitly that the momentum space eigenvalue equation for the second order Casimir operator of the de Sitter group is equivalent to a wave equation in Minkowski momentum space, which describes the mass‐spin relation of a mechanical system in Minkowski space, consisting of two equal mass, point‐like constituents rotating uniformly at a distance R from their geometric center, where R is the radius of the de Sitter space. Applications to the relativistic rotator are considered. Contrary to our previous results, we find that the relativistic rotator does not go into a structureless relativistic mass point in the elementary limit obtained by contracting the de Sitter group into the Poincaré group. Our analysis can be carried over, with relatively minor modifications, to anti‐de Sitter space, and similar results hold there. Additional physical consequences are also discussed.

Original languageEnglish (US)
Pages (from-to)629-647
Number of pages19
JournalFortschritte der Physik
Volume34
Issue number9
DOIs
StatePublished - 1986

Fingerprint

integral transformations
Minkowski space
momentum
wave equations
eigenvalues
operators
radii

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

Cite this

@article{c90698c6db7f43c1becaf3d1e5d24395,
title = "An Integral Transform in de Sitter Space",
abstract = "An integral transform on (4 + 1) de Sitter space, which is a generalization of the Fourier transform for a Dirac particle in Minkowski space, is considered, and proofs of its relevant properties are provided. With this integral transform we demonstrate explicitly that the momentum space eigenvalue equation for the second order Casimir operator of the de Sitter group is equivalent to a wave equation in Minkowski momentum space, which describes the mass‐spin relation of a mechanical system in Minkowski space, consisting of two equal mass, point‐like constituents rotating uniformly at a distance R from their geometric center, where R is the radius of the de Sitter space. Applications to the relativistic rotator are considered. Contrary to our previous results, we find that the relativistic rotator does not go into a structureless relativistic mass point in the elementary limit obtained by contracting the de Sitter group into the Poincar{\'e} group. Our analysis can be carried over, with relatively minor modifications, to anti‐de Sitter space, and similar results hold there. Additional physical consequences are also discussed.",
author = "P. Moylan",
year = "1986",
doi = "10.1002/prop.19860340903",
language = "English (US)",
volume = "34",
pages = "629--647",
journal = "Fortschritte der Physik",
issn = "0015-8208",
publisher = "Wiley-VCH Verlag",
number = "9",

}

An Integral Transform in de Sitter Space. / Moylan, P.

In: Fortschritte der Physik, Vol. 34, No. 9, 1986, p. 629-647.

Research output: Contribution to journalArticle

TY - JOUR

T1 - An Integral Transform in de Sitter Space

AU - Moylan, P.

PY - 1986

Y1 - 1986

N2 - An integral transform on (4 + 1) de Sitter space, which is a generalization of the Fourier transform for a Dirac particle in Minkowski space, is considered, and proofs of its relevant properties are provided. With this integral transform we demonstrate explicitly that the momentum space eigenvalue equation for the second order Casimir operator of the de Sitter group is equivalent to a wave equation in Minkowski momentum space, which describes the mass‐spin relation of a mechanical system in Minkowski space, consisting of two equal mass, point‐like constituents rotating uniformly at a distance R from their geometric center, where R is the radius of the de Sitter space. Applications to the relativistic rotator are considered. Contrary to our previous results, we find that the relativistic rotator does not go into a structureless relativistic mass point in the elementary limit obtained by contracting the de Sitter group into the Poincaré group. Our analysis can be carried over, with relatively minor modifications, to anti‐de Sitter space, and similar results hold there. Additional physical consequences are also discussed.

AB - An integral transform on (4 + 1) de Sitter space, which is a generalization of the Fourier transform for a Dirac particle in Minkowski space, is considered, and proofs of its relevant properties are provided. With this integral transform we demonstrate explicitly that the momentum space eigenvalue equation for the second order Casimir operator of the de Sitter group is equivalent to a wave equation in Minkowski momentum space, which describes the mass‐spin relation of a mechanical system in Minkowski space, consisting of two equal mass, point‐like constituents rotating uniformly at a distance R from their geometric center, where R is the radius of the de Sitter space. Applications to the relativistic rotator are considered. Contrary to our previous results, we find that the relativistic rotator does not go into a structureless relativistic mass point in the elementary limit obtained by contracting the de Sitter group into the Poincaré group. Our analysis can be carried over, with relatively minor modifications, to anti‐de Sitter space, and similar results hold there. Additional physical consequences are also discussed.

UR - http://www.scopus.com/inward/record.url?scp=84990727770&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84990727770&partnerID=8YFLogxK

U2 - 10.1002/prop.19860340903

DO - 10.1002/prop.19860340903

M3 - Article

AN - SCOPUS:84990727770

VL - 34

SP - 629

EP - 647

JO - Fortschritte der Physik

JF - Fortschritte der Physik

SN - 0015-8208

IS - 9

ER -