The basis for engineering electromagnetic computations still rely on Gibbs' vector algebra. It is well known that Clifford algebra (geometric algebra) presents several enhancement on the latter. By taking advantage that in the three-dimensional space Clifford algebra is isomorphic to Pauli algebra it is possible to describe all the relevant vector operations occurring in electromagnetic theory in terms of Pauli matrices. In particular it is possible to write Maxwell's equations in a form similar to the Dirac equation. In this way, instead of having six coupled equations from the curls operators, we can deal with just four linear equations. The latter can be further simplified to just two sets of two linear equations by the Weyl decomposition.

Rozzi, T., Mongiardo, M., Mastri, F., Mencarelli, D., Monti, G., Venanzoni, G. (2017). Electromagnetic field modeling through the use of Dirac matrices and geometric algebra. Institute of Electrical and Electronics Engineers Inc. [10.1109/ICEAA.2017.8065359].

Electromagnetic field modeling through the use of Dirac matrices and geometric algebra

Mastri, Franco;
2017

Abstract

The basis for engineering electromagnetic computations still rely on Gibbs' vector algebra. It is well known that Clifford algebra (geometric algebra) presents several enhancement on the latter. By taking advantage that in the three-dimensional space Clifford algebra is isomorphic to Pauli algebra it is possible to describe all the relevant vector operations occurring in electromagnetic theory in terms of Pauli matrices. In particular it is possible to write Maxwell's equations in a form similar to the Dirac equation. In this way, instead of having six coupled equations from the curls operators, we can deal with just four linear equations. The latter can be further simplified to just two sets of two linear equations by the Weyl decomposition.
2017
Proceedings of the 2017 19th International Conference on Electromagnetics in Advanced Applications, ICEAA 2017
757
760
Rozzi, T., Mongiardo, M., Mastri, F., Mencarelli, D., Monti, G., Venanzoni, G. (2017). Electromagnetic field modeling through the use of Dirac matrices and geometric algebra. Institute of Electrical and Electronics Engineers Inc. [10.1109/ICEAA.2017.8065359].
Rozzi, Tullio; Mongiardo, Mauro; Mastri, Franco; Mencarelli, Davide; Monti, Giuseppina; Venanzoni, Giuseppe
File in questo prodotto:
Eventuali allegati, non sono esposti

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/622636
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 1
  • ???jsp.display-item.citation.isi??? 1
social impact