On a connection between the Maxwell system, the extended Maxwell system, the Dirac operator and gravito-electromagnetism

Rainer Picard, Sascha Trostorff, Marcus Waurick

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

The close connection between Maxwell's equations and the Dirac equation is under consideration in a rigorous functional analytical framework. The two systems are linked via the so-called extended Maxwell system Picard R. A structural observation for linear material laws in classical mathematical physics. Mathematical Methods in the Applied Sciences 2009;32(14):1768–1803, which is here re-considered in the time-dependent case as an evolutionary space-time operator equation. This structural observation is then applied to recover and generalize the equations of gravito-electromagnetism and to reformulate theMaxwell-Dirac system as a system of three coupled extended Maxwell systems. This reformulation rests on the observation that what in electrodynamics is commonly known as 'potential' is actually a solution to another extended Maxwell system.
LanguageEnglish
Pages415-434
Number of pages20
JournalMathematical Methods in the Applied Sciences
Volume40
Issue number2
Early online date22 Dec 2014
DOIs
Publication statusPublished - 30 Jan 2017

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Electromagnetism
Maxwell System
Extended Systems
Electrodynamics
Maxwell equations
Dirac Operator
Physics
Dirac Equation
Operator Equation
Reformulation
Maxwell's equations
Paul Adrien Maurice Dirac
Space-time
Generalise
Observation

Keywords

  • Maxwell's equations
  • extended Maxwell system
  • dirac operator
  • gravito-electromagnetism
  • Maxwell–Dirac system
  • evolutionary equations

Cite this

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AB - The close connection between Maxwell's equations and the Dirac equation is under consideration in a rigorous functional analytical framework. The two systems are linked via the so-called extended Maxwell system Picard R. A structural observation for linear material laws in classical mathematical physics. Mathematical Methods in the Applied Sciences 2009;32(14):1768–1803, which is here re-considered in the time-dependent case as an evolutionary space-time operator equation. This structural observation is then applied to recover and generalize the equations of gravito-electromagnetism and to reformulate theMaxwell-Dirac system as a system of three coupled extended Maxwell systems. This reformulation rests on the observation that what in electrodynamics is commonly known as 'potential' is actually a solution to another extended Maxwell system.

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