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Pre-geometric structure of quantum and classical particles in terms of quaternion spinors
Ефремов А.П. (Yefremov A.P.) Pre-geometric structure of quantum and classical particles in terms of quaternion spinors // Gravitation and Cosmology. 2013. 19(2): 71-78. doi: 10.1134/S0202289313020047

Категории: Исследование, Авторский указатель

Pre-geometric structure of quantum and classical particles in terms of quaternion spinors
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Аннотация

It is shown that dyad vectors on a local domain of a complex-number-valued surface, when squared, form a set of four quaternion algebra units. A model of a proto-particle is built by the dyad rotation and stretching; this transformation violates the metric properties of the surface, but the defect is cured by a stability condition for a normalization functional over an abstract space. If the space is the physical one, then the stability condition is precisely the Schrödinger equation; the separated real and imaginary parts of the condition are the mass conservation equation and the Hamilton-Jacoby equation, respectively. A 3D particle (composed of proto-particle parts) should be conceived as a rotating massive point, its Lagrangian automatically becoming that of a relativistic classical particle, with energy and momentum proportional to Planck’s constant. The influence of a vector field on particle propagation causes an automatic appearance of Pauli’s spin term in the Schrödinger equation.

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