Quantum cosmology with fermionic matter

The quantum evolution of homogeneous isotropic cosmological models with ferm ionic matter described by spinor fields is investigated within the framework of the formalism of superspace quantization. The fact that quadratic combinations of fermionic operators (current density, spin density, Lagrangian, etc.) are bosonic operators and admit an explicit Schrödinger representation is used in an essential way. It is shown that the DeWitt equation for the cosmological models with fermionic matter under consideration has the form of the Schrödinger equation, so that a correct definition is possible for the probability density of the existence of the models under consideration, in which the singularity is removed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 15–19, March, 1990.