Faraday’s Form and Maxwell’s Equations in the Heisenberg Group
Identifieur interne : 000570 ( Main/Exploration ); précédent : 000569; suivant : 000571Faraday’s Form and Maxwell’s Equations in the Heisenberg Group
Auteurs : Bruno Franchi [Italie] ; Maria Carla Tesi [Italie]Source :
- Milan Journal of Mathematics [ 1424-9286 ] ; 2009-12-01.
Abstract
Abstract: In this note we present a geometric formulation of Maxwell’s equations in Carnot groups (connected simply connected nilpotent Lie groups with stratified Lie algebra) in the setting of the intrinsic complex of differential forms defined by M. Rumin. Restricting ourselves to the first Heisenberg group $${\mathbb{H}^{1}}$$ , we show that these equations are invariant under the action of suitably defined Lorentz transformations, and we prove the equivalence of these equations with differential equations “in coordinates”. Moreover, we analyze the notion of “vector potential”, and we show that it satisfies a new class of 4th order evolution differential equations.
Url:
DOI: 10.1007/s00032-009-0104-9
Affiliations:
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Donato 5, 40127, Bologna</wicri:regionArea><orgName type="university">Université de Bologne</orgName><placeName><settlement type="city">Bologne</settlement><region nuts="2" type="region">Émilie-Romagne</region></placeName></affiliation><affiliation wicri:level="1"><country wicri:rule="url">Italie</country></affiliation></author></analytic><monogr></monogr><series><title level="j">Milan Journal of Mathematics</title><title level="j" type="sub">Issued by the Seminario Matematico e Fisico di Milano</title><title level="j" type="abbrev">Milan J. Math.</title><idno type="ISSN">1424-9286</idno><idno type="eISSN">1424-9294</idno><imprint><publisher>SP Birkhäuser Verlag Basel</publisher><pubPlace>Basel</pubPlace><date type="published" when="2009-12-01">2009-12-01</date><biblScope unit="volume">77</biblScope><biblScope unit="issue">1</biblScope><biblScope unit="page" from="245">245</biblScope><biblScope unit="page" to="270">270</biblScope></imprint><idno type="ISSN">1424-9286</idno></series></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">1424-9286</idno></seriesStmt></fileDesc><profileDesc><textClass></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">Abstract: In this note we present a geometric formulation of Maxwell’s equations in Carnot groups (connected simply connected nilpotent Lie groups with stratified Lie algebra) in the setting of the intrinsic complex of differential forms defined by M. Rumin. Restricting ourselves to the first Heisenberg group $${\mathbb{H}^{1}}$$ , we show that these equations are invariant under the action of suitably defined Lorentz transformations, and we prove the equivalence of these equations with differential equations “in coordinates”. Moreover, we analyze the notion of “vector potential”, and we show that it satisfies a new class of 4th order evolution differential equations.</div></front></TEI><affiliations><list><country><li>Italie</li></country><region><li>Émilie-Romagne</li></region><settlement><li>Bologne</li></settlement><orgName><li>Université de Bologne</li></orgName></list><tree><country name="Italie"><region name="Émilie-Romagne"><name sortKey="Franchi, Bruno" sort="Franchi, Bruno" uniqKey="Franchi B" first="Bruno" last="Franchi">Bruno Franchi</name></region><name sortKey="Franchi, Bruno" sort="Franchi, Bruno" uniqKey="Franchi B" first="Bruno" last="Franchi">Bruno Franchi</name><name sortKey="Tesi, Maria Carla" sort="Tesi, Maria Carla" uniqKey="Tesi M" first="Maria Carla" last="Tesi">Maria Carla Tesi</name><name sortKey="Tesi, Maria Carla" sort="Tesi, Maria Carla" uniqKey="Tesi M" first="Maria Carla" last="Tesi">Maria Carla Tesi</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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