Les Algebres de Clifford et les transformations des multivecteurs. L’Algebre de Clifford de R(1,3) et la constante de Planck
Identifieur interne : 001E21 ( Istex/Checkpoint ); précédent : 001E20; suivant : 001E22Les Algebres de Clifford et les transformations des multivecteurs. L’Algebre de Clifford de R(1,3) et la constante de Planck
Auteurs : R. Boudet [France]Source :
- Fundamental Theories of Physics ; 1992.
Abstract
Abstract: Using a convenient form of the inner products $$ x.X,\;X.x,\;x \in E,\;X \in \Delta E,\;E = \;R^{q,n - q} $$ and considering the relations $$ x.X = \;x.X + x\Delta X,\;Xy = \;X.y + X\Delta y $$ as definitions one proves, as a theorem, the relation x(Xy) = (xX)y which allows one to construct the Clifford algebra C(E) as a multivectorial algebra. The infinitesimal operators associated with some transformations of multivectors, using specific properties of C(E), are defined and studied. As an application, a euclidean interpretation of the reduced Planck constant ℏ is drawn up in the following way. ℏ appears in the kinetic part (ℏc/2)L of the momentum-energy tensor of the Dirac particle. The tensor L is constructed a priori in a purely geometrical way, expressing a generalized ”Darboux motion“ of a plane in spacetime R 1,3.
Url:
DOI: 10.1007/978-94-015-8090-8_34
Affiliations:
Links toward previous steps (curation, corpus...)
Links to Exploration step
ISTEX:30BC8D9F66826AE9319BCAD68FD9C5FA4BD7750CLe document en format XML
<record><TEI wicri:istexFullTextTei="biblStruct"><teiHeader><fileDesc><titleStmt><title xml:lang="de">Les Algebres de Clifford et les transformations des multivecteurs. L’Algebre de Clifford de R(1,3) et la constante de Planck</title><author><name sortKey="Boudet, R" sort="Boudet, R" uniqKey="Boudet R" first="R." last="Boudet">R. Boudet</name></author></titleStmt><publicationStmt><idno type="wicri:source">ISTEX</idno><idno type="RBID">ISTEX:30BC8D9F66826AE9319BCAD68FD9C5FA4BD7750C</idno><date when="1992" year="1992">1992</date><idno type="doi">10.1007/978-94-015-8090-8_34</idno><idno type="url">https://api.istex.fr/document/30BC8D9F66826AE9319BCAD68FD9C5FA4BD7750C/fulltext/pdf</idno><idno type="wicri:Area/Istex/Corpus">000A28</idno><idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Corpus" wicri:corpus="ISTEX">000A28</idno><idno type="wicri:Area/Istex/Curation">000A28</idno><idno type="wicri:Area/Istex/Checkpoint">001E21</idno><idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Checkpoint">001E21</idno></publicationStmt><sourceDesc><biblStruct><analytic><title level="a" type="alt" xml:lang="de">Les Algebres de Clifford et les transformations des multivecteurs. L’Algebre de Clifford de R(1,3) et la constante de Planck</title><author><name sortKey="Boudet, R" sort="Boudet, R" uniqKey="Boudet R" first="R." last="Boudet">R. Boudet</name><affiliation wicri:level="4"><country xml:lang="fr">France</country><wicri:regionArea>Université de Provence, PL V. Hugo, 13331, Marseille</wicri:regionArea><placeName><region type="region" nuts="2">Provence-Alpes-Côte d'Azur</region><settlement type="city">Marseille</settlement><settlement type="city">Marseille</settlement></placeName><orgName type="university">Université de Provence</orgName></affiliation></author></analytic><monogr></monogr><series><title level="s">Fundamental Theories of Physics</title><imprint><date>1992</date></imprint></series></biblStruct></sourceDesc></fileDesc><profileDesc><textClass></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">Abstract: Using a convenient form of the inner products $$ x.X,\;X.x,\;x \in E,\;X \in \Delta E,\;E = \;R^{q,n - q} $$ and considering the relations $$ x.X = \;x.X + x\Delta X,\;Xy = \;X.y + X\Delta y $$ as definitions one proves, as a theorem, the relation x(Xy) = (xX)y which allows one to construct the Clifford algebra C(E) as a multivectorial algebra. The infinitesimal operators associated with some transformations of multivectors, using specific properties of C(E), are defined and studied. As an application, a euclidean interpretation of the reduced Planck constant ℏ is drawn up in the following way. ℏ appears in the kinetic part (ℏc/2)L of the momentum-energy tensor of the Dirac particle. The tensor L is constructed a priori in a purely geometrical way, expressing a generalized ”Darboux motion“ of a plane in spacetime R 1,3.</div></front></TEI><affiliations><list><country><li>France</li></country><region><li>Provence-Alpes-Côte d'Azur</li></region><settlement><li>Marseille</li></settlement><orgName><li>Université de Provence</li></orgName></list><tree><country name="France"><region name="Provence-Alpes-Côte d'Azur"><name sortKey="Boudet, R" sort="Boudet, R" uniqKey="Boudet R" first="R." last="Boudet">R. Boudet</name></region></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
EXPLOR_STEP=$WICRI_ROOT/Wicri/Mathematiques/explor/BourbakiV1/Data/Istex/Checkpoint
HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 001E21 | SxmlIndent | more
Ou
HfdSelect -h $EXPLOR_AREA/Data/Istex/Checkpoint/biblio.hfd -nk 001E21 | SxmlIndent | more
Pour mettre un lien sur cette page dans le réseau Wicri
{{Explor lien
|wiki= Wicri/Mathematiques
|area= BourbakiV1
|flux= Istex
|étape= Checkpoint
|type= RBID
|clé= ISTEX:30BC8D9F66826AE9319BCAD68FD9C5FA4BD7750C
|texte= Les Algebres de Clifford et les transformations des multivecteurs. L’Algebre de Clifford de R(1,3) et la constante de Planck
}}
| This area was generated with Dilib version V0.6.33. |  |