Abstract
The (generalized) Fierz identities are shown to reduce to a single equation, a relation between the elements of a multivector Clifford algebra. For this purpose we use a multivectorial generalization of the spinors to vectors Cartan’s map. The method is put in a general form such that the vectors correspond to spacetime as a base space and isotopic symmetries, represented as a multivector group, are also included. A particular case is the representation of spacetime by its even part Clifford algebra only, through quaternions. This subalgebra is projected and analyzed.
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© 1992 Springer Science+Business Media Dordrecht
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Rodríguez-Romo, S., Viniegra, F., Keller, J. (1992). Geometrical content of the Fierz identities. In: Micali, A., Boudet, R., Helmstetter, J. (eds) Clifford Algebras and their Applications in Mathematical Physics. Fundamental Theories of Physics, vol 47. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8090-8_45
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DOI: https://doi.org/10.1007/978-94-015-8090-8_45
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-4130-2
Online ISBN: 978-94-015-8090-8
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