Geodesic
A method of algebraic extension of the Lagrangian of weak interactions to non-associative algebra
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2011), pp. 3-11

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We propose an algebraic approach to the extension of the Lagrangian of weak interactions onto a non-associative algebra. A special feature of the proposed method is the use of matrix representations (rather than vector ones) for physical fields and their interactions. We construct the Lagrangian of material and interaction fields on the introduced algebra.
Keywords: quantum field theory, Cayley octaves, octonions, weak interactions, non-associativity. 
V. Yu. Dorofeev. A method of algebraic extension of the Lagrangian of weak interactions to non-associative algebra. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2011), pp. 3-11. http://geodesic.mathdoc.fr/item/IVM_2011_11_a0/
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[1] Baez J. C., “The octonions”, Bull. Amer. Math. Soc., 39:2 (2002), 145–205, arXiv: math/0105155 | DOI | MR | Zbl

[2] Jordan P., Neumann J., Wigner E., “On an algebraic generalization of the quantum mechanical formalism”, Ann. Math., 35 (1934), 29–64 | DOI | MR | Zbl

[3] Zorn M., “Alternativkorper und quadratische Systeme”, Abh. Math. Sem. Hamb. Univ., 9 (1933), 395–402 | DOI | Zbl

[4] Daboul J., Delbourgo R., “Matrix representation of octonions and generalizations”, J. Math. Phys., 40:8 (1999), 4134–4150, arXiv: hep-th/9906065 | DOI | MR | Zbl

[5] Nelipa N. F., Fizika elementarnykh chastits. Kalibrovochnye polya, Nauka, M., 1985 | MR