Spin Precession of Slow Neutrons in Einstein–Cartan Gravity with Torsion, Chameleon and Magnetic Field

We analyse a spin precession of slow neutrons in the Einstein–Cartan gravity with torsion, chameleon and magnetic field. For the derivation of the Heisenberg equation of motion of the neutron spin we use the effective low–energy potential, derived by Ivanov and Wellenzohn (Phys. Rev. D 92, 125004 (2015)) for slow neutrons, coupled to gravitational, chameleon and torsion fields to order 1/m, where m is the neutron mass. In addition to this low–energy interactions we switch on the interaction of slow neutrons with a magnetic field. We show that to linear order approximation with respect to gravitational, chameleon and torsion fields the Dirac Hamilton operator for fermions (neutrons), moving in spacetimes created by rotating coordinate systems, contains the anti–Hermitian operators of torsion–fermion (neutron) interactions, caused by torsion scalar and tensor space–space–time and time–space–space degrees of freedom. Such anti–Hermitian operators violate CP and T invariance. In the low–energy approximation the CP and T violating torsion– fermion (neutron) interactions appear only to order O(1/m). One may assume that in the rotating Universe and galaxies the obtained anti–Hermitian torsion–fermion interactions might be an origin of i) violation of CP and T invariance in the Universe and ii) of baryon asymmetry. We show that anti–Hermitian torsion–fermion interactions of relativistic fermions, violating CP and T invariance, i) cannot be removed by non–unitary transformations of the Dirac fermion wave functions and ii) are conformal invariant. According to general requirements of conformal invariance of massive particle theories in gravitational fields (see R. H. Dicke, Phys. Rev. 125, 2163 (1962) and A. J. Silenko, Phys. Rev. D 91, 065012 (2015)), conformal invariance of anti–Hermitian torsion–fermion interactions is valid only if the fermion mass is changed by a conformal factor.