Abstract
The concept of the Q field is introduced as a 2×2 matrix representation of the variable basis of vectors satisfying the rule of multiplication of quaternion imaginary numbers and as an element of the group of transformations of the basis preserving the invariance of this multiplication rule. The rule for projecting such matrices on a given direction is determined with the help of the characteristic functions of the matrices-vectors of the Q field. The differential structure of Q fields is studied. The theory developed is illustrated by an example of a model-topological classification of particles according to the magnitude of their spin.
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G. Kazanov, Vector Algebra [Russian translation], Mir, Moscow (1979).
A. P. Yefremov, Lett. Nuovo Cim.,37, 315 (1983).
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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 14–18, December, 1985.
The author thanks Robert M. Keene, Professor at the University of Houston, for assistance and attention during the author's stay in the USA.
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Efremov, A.P. The Q field, a variable quaternion basis. Soviet Physics Journal 28, 961–964 (1985). https://doi.org/10.1007/BF00899083
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DOI: https://doi.org/10.1007/BF00899083