Secondary quantization of the Dirac free field in hypercomplex system of numbers

The method of secondary quantization of the Dirac free field is developed in the formalism of a hypercomplex system of numbers, generalizing the Clifford algebra to state space analogously to its generalization to distorted space. Then, after conversion to a new basis, it is shown that, taking account of the projection operators, the bases of Fermi algebra — creation and annihilation operators — may be taken as the new basis. Writing the solution of the Dirac free equation in the new basis, the physically observed field values are written in terms of secondary-quantization operators. The adjustable Dirac-field function is calculated in the same formalism.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 93–97, October, 1989.