Nonassociative Geometry of Special Relativity
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The nonassociative axiomatics of the relativistic law of composition of velocities in special relativity is presented. For the first time the canomical unary operations are considered.
KeywordsField Theory Elementary Particle Quantum Field Theory Special Relativity Unary Operation
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- Fok, Vladimir A. (1955). The Theory of Space, Time and Gravitation, (in Russian) GITTL, Moscow. English translation, Pergamon Press (1959) MR21 #7042.Google Scholar
- Nesterov, Alexander I. (1989). The methods of nonassociative algebra in physics, Doctor of Sciences Dissertation, Institute of Physics of Estonian Academy of Sciences, Tartu.Google Scholar
- Sabinin, Lev V. (1981). Methods of nonassociative algebra in differential geometry, in: Shoshichi Kobayashi and Katsumi Nomizy, Foundations of Differential Geometry, [in Russian], Nauka, Moscow, Vol. 1, Supplement, pp. 293–339; MR 84b:53002.Google Scholar
- Sabinin, Lev V. (1991). Analytic Quasigroups and Geometry, Friendship of Nations University, Moscow.Google Scholar
- Sabinin, Lev V. (1995). On gyrogroups of Ungar, Advances in Mathematical Sciences, 50(5), 251–252 [in Russian]; English translation: Russian Mathematical Survey, 50(5).Google Scholar
- Sabinin, Lev V. (1999). Smooth Quasigroups and Loops, Kluwer, Dordrecht.Google Scholar
- Sabinin, Lev V., and P. O. Miheev (1993). On the law of addition of velocities in special relativity, Advances in Mathematical Sciences, 48(5), 183–184 [in Russian]. English translation: Russian Mathematical Survey, 48(5).Google Scholar
- Sabinin, Lev V., and Alexander I. Nesterov (1997). Smooth loops and Thomas precession, Hadronic Journal, 20, 219–237.Google Scholar
- Sabinin, Lev V., Ludmila L. Sabinina, and Larissa V. Sbitneva (1998). On the notion of gyrogroup, Aequationes Mathematicae, 56(1), 11–17.Google Scholar
- Sabinin, Lev V., and Larissa V. Sbitneva (1994). Half Bol loops, in: Webs and Quasigroups, Tver University Press, pp. 50–54.Google Scholar
- Ungar, Abraham A. (1990). Weakly associative groups, Results in Mathematics, 17, 149–168.Google Scholar
- Ungar, Abraham A. (1994). The holomorphic automorphism group of the complex disk, Aequationes Mathematicae, 17(2), 240–254.Google Scholar
- Ungar, Abraham A. (1997). Thomas precession: Its underlying gyrogroup axioms and their use in hyperbolic geometry and relativistic physics, Foundations of Physics, 27, 881–951.Google Scholar
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