Abstract
We consider a case in which the octonionic observables form a Jordan Algebra. Then the automorphism group turns out to be an exceptional group F 4 or E 6 and we are led to a gauge field theory of quarks and leptons based on exceptional groups. Some relations of octonion and split octonion algebras and their relation to algebra of quarks are explicitly shown.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Catto, S., Choun, Y.: Acta Polytechnica 51, 77 (2011)
Chevalley, C., Schafer, R.D.: Proc. Natl. Acad. Sci. USA 36, 137 (1950)
Schafer, R.D.: An Introduction to Non-associative Algebras. Academic Press, New York (1966)
Günaydin, M., Gürsey, F.: Phys. Rev. D9, 3387 (1974)
Gürsey, F., Ramond, P., Sikivie, P.: Phys. Lett. 60B, 177 (1976)
Günaydin, M.: The exceptional superspace and the quadratic jordan formulation of quantum mechanics. In: Schwarz, J.H. (ed.) Elementary Particles and the Universe: Essays in Honor of Murray Gell-Mann, pp. 99–119. Cambridge University Press, Cambridge (1991)
Faulkner, J.R.: Memoirs of the American Mathematical Society, vol. 104. American Mathematical Society, Providence, RI (1970)
Gürsey, F., Marchildon, L.: J. Math. Phys. 19, 942 (1977)
Kac, V.: Comm. Math. Phys. 53, 31 (1977)
Acknowledgements
The development of the ideas presented here is due in a large part to stimulating discussions with our colleagues and friends including Vladimir Akulov, Vladimir Dobrev, Francesco Iachello, Ramzi Khuri, Pierre Ramond and late Feza Gürsey. One of us (SC) would like to thank Professor Dobrev for invitation to give a talk Varna on the subject of this paper.This work was supported in part by DOE contracts No. DE-AC-0276-ER 03074 and 03075; NSF Grant No. DMS-8917754.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer Japan
About this paper
Cite this paper
Catto, S., Choun, Y.S., Kurt, L. (2013). Invariance Properties of the Exceptional Quantum Mechanics (F 4) and Its Generalization to Complex Jordan Algebras (E 6). In: Dobrev, V. (eds) Lie Theory and Its Applications in Physics. Springer Proceedings in Mathematics & Statistics, vol 36. Springer, Tokyo. https://doi.org/10.1007/978-4-431-54270-4_34
Download citation
DOI: https://doi.org/10.1007/978-4-431-54270-4_34
Published:
Publisher Name: Springer, Tokyo
Print ISBN: 978-4-431-54269-8
Online ISBN: 978-4-431-54270-4
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)