Physical aspects of the space–time torsion

Abstract

We review many quantum aspects of torsion theory and discuss the possibility of the space–time torsion to exist and to be detected. The paper starts, in Section 2, with a pedagogical introduction to the classical gravity with torsion, that includes also interaction of torsion with matter fields. Special attention is paid to the conformal properties of the theory. In Section 3, the renormalization of quantum theory of matter fields and related topics, like renormalization group, effective potential and anomalies, are considered. Section 4 is devoted to the action of spinning and spinless particles in a space–time with torsion, and to the discussion of possible physical effects generated by the background torsion. In particular, we review the upper bounds for the magnitude of the background torsion which are known from the literature. In Section 5, the comprehensive study of the possibility of a theory for the propagating completely antisymmetric torsion field is presented. It is supposed that the propagating field should be quantized, and that its quantum effects must be described by, at least, some effective low-energy quantum field theory. We show, that the propagating torsion may be consistent with the principles of quantum theory only in the case when the torsion mass is much greater than the mass of the heaviest fermion coupled to torsion. Then, universality of the fermion–torsion interaction implies that torsion itself has a huge mass, and cannot be observed in realistic experiments. Thus, the theory of quantum matter fields on the classical torsion background can be formulated in a consistent way, while the theory of dynamical torsion meets serious obstacles. In Section 6, we briefly discuss the string-induced torsion and the possibility to induce torsion action and torsion itself through the quantum effects of matter fields.