Spin precession of slow neutrons in Einstein-Cartan gravity with torsion, chameleon, and magnetic field

Abstract

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 torsionfermion (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.

Quantum hydrodynamics of spinning particles in electromagnetic and torsion fields

“…These results are consistent with the alternative empirical estimates for the torsion limits [29][30][31][32][33][34][35][36][37][38]. As another powerful tool one can mention the use of the quantum interferometry to probe the spacetime structure, including the search for possible post-Riemannian deviations, focusing on the detection of the phase shift and polarization rotation effects for the neutron and atom beams [55][56][57][58][59].…”

“…Experimental search for the nontrivial torsion effects is naturally embedded into the broader framework of the studies of the spin-dependent long-range forces [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38]. By making use of the corresponding experimental techniques, it is possible to find strong limits on the values of the gauge gravity spin-torsion coupling constants and on the torsion field itself.…”

“…The study of the spin-torsion coupling obviously fits into the general context of the theoretical and experimental research of spin-dependent long-range forces [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38]. Certain extensions of the Standard Model in the high energy particle physics predict the existence of new particles, in particular, of the light pseudoscalar bosons (such as goldstones, axions [39][40][41], arions [42,43], etc) that may give rise to the spin-spin interactions of various kinds.…”

“…An interesting practical realization of theoretical findings has been recently proposed as a new Gravity Probe Spin space mission using mmscale ferromagnetic gyroscopes in orbit around the Earth [28]. Typically, the predicted spin-torsion effects are expected to be quite small and difficult to observe experimentally, however, one can set the experimental bounds on the spin-torsion coupling constants and on the torsion field as well [29][30][31][32][33][34][35][36][37][38].…”

Does space-time torsion determine the minimum mass of gravitating particles?

“…The effects of torsion in the framework of Einstein-Cartan theory in early-Universe cosmology were investigated in [21], while the gravitational collapse of a homogeneous Weyssenhoff fluid sphere, in the presence of a negative cosmological constant, was considered in [22]. For recent investigations of the cosmology and astrophysics of Einstein-Cartan theory see [23][24][25][26][27][28][29][30][31][32]. In [33] it was shown that by enlarging the EinsteinCartan Lagrangian with suitable kinetic terms quadratic in the gravitational gauge field strengths (torsion and curvature) one can obtain some new, massive propagating gravitational degrees of freedom.…”