THE DIFFERENTIAL ALGEBRA OF BIQUATERNIONS IN EQUATIONS OF MATHEMATICAL AND THEORETICAL PHYSICS
2012jzq | Alexeyeva L.A.  // Institute of mathematics and mathematical modelling, Almaty, Kazakhstan, alexeeva@math.kz

The functional space of biquaternions is considered on Minkovskiy space. Here the scalar-vector biquaternions representation is used which was offered by W. Hamilton for quaternions. With introduction of differential operator - a mutual complex gradient (bigradients), which generalize the notion of a gradient on biquaternions space, biquaternionic wave (biwave) equations are considered, their invariance for group of the Lorence-Puancare transformations is proved and their generalized solutions have been obtained. Biquaternionic form of generalized Maxwell-Dirac equation is constructed and its decisions are researched on base of the differential biquaternions algebra. Its generalized decisions are built with use of scalar potential. The new equation for these potential are constructed which unites known equations of quantum mechanics (Klein-Gordon and Schrodinger Eq.). The nonstationary, steady-state and harmonic on time scalar fields and generated by them the spinors and spinors fields in biquaternionic form are constructed.

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