We investigate the motion of spinning test bodies in General Relativity. By means of a multipolar approximation method for extended test bodies we derive the equations of motion and classify the orbital motion of pole-dipole test bodies in the equatorial plane of the Kerr geometry. An exact expression for the periastron shift of a spinning test body is given. Implications of test body spin corrections are studied and compared with the results obtained by means of other approximation schemes.

We study the quantum mechanics of a Dirac fermion on a curved spacetime manifold. The metric of the spacetime is completely arbitrary, allowing for the discussion of all possible inertial and gravitational field configurations. In this framework, we find the Hermitian Dirac Hamiltonian for an arbitrary classical external field (including the gravitational and electromagnetic ones). In order to discuss the physical content of the quantum-mechanical model, we further apply the Foldy-Wouthuysen transformation, and derive the quantum equations of motion for the spin and position operators. We analyze the semiclassical limit of these equations and compare the results with the dynamics of a classical particle with spin in the framework of the standard Mathisson-Papapetrou theory and in the classical canonical theory. The comparison of the quantum-mechanical and classical equations of motion of a spinning particle in an arbitrary gravitational field shows their complete agreement.

We discuss the quantum dynamics of a Dirac fermion particle in the Poincaré gauge gravitational field. The minimal as well as the Pauli-type nonminimal coupling of a fermion with external fields is studied, bringing into consideration the notions of the translational and the Lorentz gravitational moments. The anomalous gravitomagnetic and gravitoelectric moments are ruled out on the basis of the covariance arguments. We derive the general Foldy-Wouthuysen transformation for an arbitrary configuration of the Poincaré gauge gravitational field without assuming it is weak. Making use of the Foldy-Wouthuysen Hamiltonian for the Dirac particle coupled to a magnetic field in a noninertial reference system, we analyze the recent experimental data and obtain bounds on the spacetime torsion.

During the conference Teleparallel Universes in Salamanca, we became aware of a recent paper [M. Fontanini, E. Huguet, and M. Le Delliou, Phys. Rev. D 2019, 99, 064006] in which some criticisms on the interpretation of teleparallel gravity as a gauge theory for the translation group were put forward. This triggered a discussion about the arguments on which those criticisms were based, whose output is described in the present paper. The main conclusion is that to a great extent, those arguments are incorrect, and lack mathematical and physical support.

We develop the general theory of spinning particles with electric and magnetic dipole moments moving in arbitrary electromagnetic, inertial, and gravitational fields. Both the quantum-mechanical and classical dynamics is investigated. We start from the covariant Dirac equation extended to a spin-$\frac{1}{2}$ fermion with anomalous magnetic and electric dipole moments and then perform the relativistic Foldy-Wouthuysen transformation. This transformation allows us to obtain the quantum-mechanical equations of motion for the physical operators in the Schrödinger form and to establish the classical limit of relativistic quantum mechanics. The results obtained are then compared to the general classical description of the spinning particle interacting with electromagnetic, inertial and gravitational fields. The complete agreement between the quantum mechanics and the classical theory is proven in the general case. As an application of the results obtained, we consider the dynamics of a spinning particle in a gravitational wave and analyze the prospects of using the magnetic resonance setup to find possible manifestations of the gravitational wave on spin.

We derive the exact gravitational wave solutions in a general class of quadratic Poincaré gauge gravity models. The Lagrangian includes all possible linear and quadratic invariants constructed from the torsion and the curvature, including the parity odd terms. The Ansatz for the gravitational wave configuration and the properties of the wave solutions are patterned following the corresponding Ansatz and the properties of the plane-fronted electromagnetic wave.