Maxwell's Equations

Maxwell's Equations

We express Maxwell's equations as a single equation, first using the divergence of a special type of matrix field to obtain the four current, and then the divergence of a special matrix to obtain the Electromagnetic field. These two equations give rise to a remarkable dual set of equations in w...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
1. Verfasser: Gottlieb, Daniel Henry
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics - Mathematical Physics
Physics - Mathematical Physics
Online-Zugang:Volltext bestellen
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page
container_issue
container_start_page
container_title
container_volume
creator Gottlieb, Daniel Henry
description We express Maxwell's equations as a single equation, first using the divergence of a special type of matrix field to obtain the four current, and then the divergence of a special matrix to obtain the Electromagnetic field. These two equations give rise to a remarkable dual set of equations in which the operators become the matrices and the vectors become the fields. The decoupling of the equations into the wave equation is very simple and natural. The divergence of the stress energy tensor gives the Lorentz Law in a very natural way. We compare this approach to related descriptions of Maxwell's equations by biquaternions and Clifford algebras.
doi_str_mv 10.48550/arxiv.math-ph/0409001
format Article
fullrecord <record><control><sourceid>arxiv_GOX</sourceid><recordid>TN_cdi_arxiv_primary_math_ph_0409001</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>math_ph_0409001</sourcerecordid><originalsourceid>FETCH-LOGICAL-a771-808587d67046b807e70df1586fc92fea05383255e5debb16d0ee3bc68704e7e23</originalsourceid><addsrcrecordid>eNotzrkOgkAUheFpLAxa2RsLEyvgDsMslIbgkmBs6MkAl0ACioCKb-9Gdar_5CNkScFyFedg63YoH1at-8JsChtc8ADolCxOenhiVW26VXC76768XroZmeS66nA-rkGiXRD5BzM874_-NjS1lNRUoLiSmZDgikSBRAlZTrkSeeo5OWrgTDGHc-QZJgkVGSCyJBXqE6BEhxlk_b_90eKmLWvdvuIvMW6KeCSyN7g6N1M</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Maxwell's Equations</title><source>arXiv.org</source><creator>Gottlieb, Daniel Henry</creator><creatorcontrib>Gottlieb, Daniel Henry</creatorcontrib><description>We express Maxwell's equations as a single equation, first using the divergence of a special type of matrix field to obtain the four current, and then the divergence of a special matrix to obtain the Electromagnetic field. These two equations give rise to a remarkable dual set of equations in which the operators become the matrices and the vectors become the fields. The decoupling of the equations into the wave equation is very simple and natural. The divergence of the stress energy tensor gives the Lorentz Law in a very natural way. We compare this approach to related descriptions of Maxwell's equations by biquaternions and Clifford algebras.</description><identifier>DOI: 10.48550/arxiv.math-ph/0409001</identifier><language>eng</language><subject>Mathematics - Mathematical Physics ; Physics - Mathematical Physics</subject><creationdate>2004-08</creationdate><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,776,881</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/math-ph/0409001$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.math-ph/0409001$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Gottlieb, Daniel Henry</creatorcontrib><title>Maxwell's Equations</title><description>We express Maxwell's equations as a single equation, first using the divergence of a special type of matrix field to obtain the four current, and then the divergence of a special matrix to obtain the Electromagnetic field. These two equations give rise to a remarkable dual set of equations in which the operators become the matrices and the vectors become the fields. The decoupling of the equations into the wave equation is very simple and natural. The divergence of the stress energy tensor gives the Lorentz Law in a very natural way. We compare this approach to related descriptions of Maxwell's equations by biquaternions and Clifford algebras.</description><subject>Mathematics - Mathematical Physics</subject><subject>Physics - Mathematical Physics</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2004</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotzrkOgkAUheFpLAxa2RsLEyvgDsMslIbgkmBs6MkAl0ACioCKb-9Gdar_5CNkScFyFedg63YoH1at-8JsChtc8ADolCxOenhiVW26VXC76768XroZmeS66nA-rkGiXRD5BzM874_-NjS1lNRUoLiSmZDgikSBRAlZTrkSeeo5OWrgTDGHc-QZJgkVGSCyJBXqE6BEhxlk_b_90eKmLWvdvuIvMW6KeCSyN7g6N1M</recordid><startdate>20040831</startdate><enddate>20040831</enddate><creator>Gottlieb, Daniel Henry</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20040831</creationdate><title>Maxwell's Equations</title><author>Gottlieb, Daniel Henry</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a771-808587d67046b807e70df1586fc92fea05383255e5debb16d0ee3bc68704e7e23</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2004</creationdate><topic>Mathematics - Mathematical Physics</topic><topic>Physics - Mathematical Physics</topic><toplevel>online_resources</toplevel><creatorcontrib>Gottlieb, Daniel Henry</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Gottlieb, Daniel Henry</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Maxwell's Equations</atitle><date>2004-08-31</date><risdate>2004</risdate><abstract>We express Maxwell's equations as a single equation, first using the divergence of a special type of matrix field to obtain the four current, and then the divergence of a special matrix to obtain the Electromagnetic field. These two equations give rise to a remarkable dual set of equations in which the operators become the matrices and the vectors become the fields. The decoupling of the equations into the wave equation is very simple and natural. The divergence of the stress energy tensor gives the Lorentz Law in a very natural way. We compare this approach to related descriptions of Maxwell's equations by biquaternions and Clifford algebras.</abstract><doi>10.48550/arxiv.math-ph/0409001</doi><oa>free_for_read</oa></addata></record>
fulltext fulltext_linktorsrc
identifier DOI: 10.48550/arxiv.math-ph/0409001
ispartof
issn
language eng
recordid cdi_arxiv_primary_math_ph_0409001
source arXiv.org
subjects Mathematics - Mathematical Physics
Physics - Mathematical Physics
title Maxwell's Equations
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-02-02T16%3A36%3A36IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-arxiv_GOX&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Maxwell's%20Equations&rft.au=Gottlieb,%20Daniel%20Henry&rft.date=2004-08-31&rft_id=info:doi/10.48550/arxiv.math-ph/0409001&rft_dat=%3Carxiv_GOX%3Emath_ph_0409001%3C/arxiv_GOX%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true