### Abstract

Original language | English |
---|---|

Pages (from-to) | 415-434 |

Number of pages | 20 |

Journal | Mathematical Methods in the Applied Sciences |

Volume | 40 |

Issue number | 2 |

Early online date | 22 Dec 2014 |

DOIs | |

Publication status | Published - 30 Jan 2017 |

### Fingerprint

### Keywords

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

### Cite this

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*Mathematical Methods in the Applied Sciences*, vol. 40, no. 2, pp. 415-434. https://doi.org/10.1002/mma.3378

**On a connection between the Maxwell system, the extended Maxwell system, the Dirac operator and gravito-electromagnetism.** / Picard, Rainer; Trostorff, Sascha; Waurick, Marcus.

Research output: Contribution to journal › Article

TY - JOUR

T1 - On a connection between the Maxwell system, the extended Maxwell system, the Dirac operator and gravito-electromagnetism

AU - Picard, Rainer

AU - Trostorff, Sascha

AU - Waurick, Marcus

PY - 2017/1/30

Y1 - 2017/1/30

N2 - 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.

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.

KW - Maxwell's equations

KW - extended Maxwell system

KW - dirac operator

KW - gravito-electromagnetism

KW - Maxwell–Dirac system

KW - evolutionary equations

UR - http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1099-1476

U2 - 10.1002/mma.3378

DO - 10.1002/mma.3378

M3 - Article

VL - 40

SP - 415

EP - 434

JO - Mathematical Methods in the Applied Sciences

JF - Mathematical Methods in the Applied Sciences

SN - 0170-4214

IS - 2

ER -