Authors

Title

Clifford algebra Cl3(C) for applications to field theories

In

International Journal of Theoretical Physics

Volume

50

Issue

10

Pages

3186–3204

Publisher

Springer

Year

2011

Indexed by

Abstract

The multivectorial algebras present yet both an academic and a technological interest.
Difficulties can occur for their use. Indeed, in all applications care is taken to distinguish
between polar and axial vectors and between scalars and pseudo scalars. Then a total
of eight elements are often considered even if they are not given the correct name of multivectors.
Eventually because of their simplicity, only the vectorial algebra or the quaternions
algebra are explicitly used for physical applications. Nevertheless, it should be more convenient
to use directly more complex algebras in order to have a wider range of application.
The aim of this paper is to inquire into one particular Clifford algebra which could solve
this problem. The present study is both didactic concerning its construction and pragmatic
because of the introduced applications. The construction method is not an original one. But
this latter allows to build up the associated real algebra as well as a peculiar formalism that
enables a formal analogy with the classical vectorial algebra. Finally several fields of the
theoretical physics will be described thanks to this algebra, as well as a more applied case in
general relativity emphasizing simultaneously its relative validity in this particular domain
and the easiness of modeling some physical problems.

Affiliations

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