### Matter and electromagnetic fields: remarks on the dualistic and unitarian standpoints

DOI: http://dx.doi.org/10.12775/TMNA.2005.002

#### Abstract

The study of the relation of matter and the electromagnetic

field is a

classical, intriguing problem both from physical and mathematical point of

view. This relation can be interpreted

from two different standpoints which, following

[M. Born and L. Infeld, < i> Foundations of the new field theory< /i> , Proc. Roy. Soc. London

Ser. A < b> 144< /b> (1934), 425–451], are called

< i> unitarian standpoint< /i> and < i> dualistic standpoint< /i> .< /p>

< p> In this paper we briefly describe two models which are related to the

unitarian and the dualistic standpoint respectively. For each model it is

possible to prove the existence of solitary waves which can be interpreted as

matter particles.

field is a

classical, intriguing problem both from physical and mathematical point of

view. This relation can be interpreted

from two different standpoints which, following

[M. Born and L. Infeld, < i> Foundations of the new field theory< /i> , Proc. Roy. Soc. London

Ser. A < b> 144< /b> (1934), 425–451], are called

< i> unitarian standpoint< /i> and < i> dualistic standpoint< /i> .< /p>

< p> In this paper we briefly describe two models which are related to the

unitarian and the dualistic standpoint respectively. For each model it is

possible to prove the existence of solitary waves which can be interpreted as

matter particles.

#### Keywords

Maxwell equations; variational principles; solitary waves

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