Four-fermion interaction as a quantum source of a twisting field

The twisting of space can be represented as a bound state of matter fields. In this approach, the Einstein-Cartan theory arises in a model for an approximate quantization of the four-fermion interaction. The twisting field is a collective field similar in nature to a field of Cooper pairs. There is no classical twisting field in the theory. The square of the twisting field is nonzero.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 7–12, January, 1985.We wish to thank V. N. Ponomarev, V. Ts. Gurovich, A. A. Starobinskii, and all the participants of the scientific seminar of D. D. Ivanenko for stimulating discussions.