Applied Physics and Mathematics Annotation << Back Quaternion algebra and the description of spin M.A. Mikaelyan In non-relativistic quantum mechanics the particle with spin ½ is associated with the evolution of four real functions, which combine with each other in two complex functions that form a spinor. With the help of quaternion algebra an alternative variant of combining in one quaternion function is considered [1]. Ultimately a description of spin particle appears to be identical to the description of spinless particle; in all formulas instead of the usual imaginary unit the quaternion imaginary unit figures. At the same time, unlike standard description, «switching» of magnetic field by the use of well-known substitution in momentum operator leads to the correct value of intrinsic magnetic moment of the particle. Relativistic generalization of the description of spin particle is formulated and corresponds to the usage of biquaternion algebra (biquaternion is a quaternion with complex components). As in non-relativistic case the wave function is a one-component quantity. It means an absence of matrices in the formalism; this fact considerably simplifies the consideration. In the language of biquaternion algebra the Dirac and Klein-Gordon equations are formulated. Simultaneously the quaternion formulation of Lorentz transformations and Maxwell equations are represented. Keywords: quantum mechanics, spin, quaternion, biquaternion, Pauli equation, Dirac equation. Contacts: E-mail: mikhail@bk.ru Pp. 76-84.