The foundations of non-associative classical field theory

Курдгелаидзе, Д. Ф.

doi:10.1007/bf03155852

Cited by 18 publications

(4 citation statements)

References 4 publications

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“…Since their discovery in 1844-1845 there have been various attempts to find appropriate uses for octonions in physics (see reviews [4][5][6][7]). One can point to the possible impact of octonions on: Color symmetry [8,9]; GUTs [10][11][12]; Representation of Clifford algebras [13,14]; Quantum mechanics [15,16]; Space-time symmetries [17,18]; Formulations of wave equations [19][20][21]; Quantum Hall effect [22]; Kaluza-Klein program without extra dimensions [23,24]; Strings and M-theory [25][26][27][28][29]; SUSY [30][31][32][33]; etc.…”

Section: Introductionmentioning

confidence: 99%

Split Octonions and Triality in (4+4)-Space

Gogberashvili¹,

Gurchumelia²

2020

Preprint

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The known equivalence of 8-dimensional chiral spinors and vectors is discussed for (4+4)space within the context of the algebra of the split octonions. It is shown that the complete algebra of hyper-complex octonionic basis units can be recovered from the Moufang and Malcev relations for the three vector-like elements of the split octonions. Trilinear form, which is invariant under SO(4,4) transformations for vectors and corresponding Spin(4,4) transformations for spinors, is explicitly written using both purely matrix and purely octonionic representations.

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Section: Introductionmentioning

confidence: 99%

Split Octonions and Triality in (4+4)-Space

Gogberashvili¹,

Gurchumelia²

2020

Preprint

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“…Representation of Clifford algebras [5]; Quantum mechanics [6]; Space-time symmetries [7]; Field theory [8]; Formulations of wave equations [9]; Quantum Hall effect [10]; Kaluza-Klein program without extra dimensions [11]; Strings and M-theory [12]; etc.…”

Section: Introductionmentioning

confidence: 99%

Rotations in the Space of Split Octonions

Gogberashvili

2009

Advances in Mathematical Physics

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The geometrical application of split octonions is considered. The modified Fano graphic, which represents products of the basis units of split octonionic, having David's Star shape, is presented. It is shown that active and passive transformations of coordinates in octonionic '8-space' are not equivalent. The group of passive transformations that leave invariant the norm of split octonions is SO(4, 4), while active rotations is done by the direct product of O(3, 4)-boosts and real non-compact form of the exceptional group G 2 . In classical limit these transformations reduce to the standard Lorentz group.

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“…Since their discovery, almost three decades before Maxwell's equations, there have been various attempts to find appropriate uses for octonions in physics (see reviews [5]). One can point to the possible impact of octonions on: Color symmetry [6]; GUTs [7]; Representation of Clifford algebras [8]; Quantum mechanics [9]; Space-time symmetries [10]; Field theory [11]; Formulations of wave equations [12]; Quantum Hall effect [13]; Strings and M-theory [14], etc.…”

Section: Introductionmentioning

confidence: 99%