Abstract:
Covariant generalizations of well-known wave equations predict the existence of inertial-gravitational effects for a variety of quantum systems that range from Bose-Einstein condensates to particles in accelerators. Additional effects arise in models that incorporate Born reciprocity principle and the notion of a maximal acceleration. Some specific examples are discussed in detail.

Abstract:
We give a solution of the wave equation for massless, or massive spin-2 particles propagating in a gravitational background. The solution is covariant, gauge-invariant and exact to first order in the background gravitational field. The background contribution is confined to a phase factor from which geometrical and physical optics can be derived. The phase also describes Mashhoon's spin-rotation coupling and, in general, the spin-gravity interaction.

Abstract:
A recently reported discrepancy between experimental and theoretical values of the muon's g-2 factor is interpreted as due to small violations of the conservation of P and T in the spin-rotation coupling. The experiments place an upper limit on these violations and on the weight change of spinning gyroscopes.

Abstract:
A quantum mechanical limit on the speed of orthogonality evolution justifies the last remaining assumption in Caianiello's derivation of the maximal acceleration. The limit is perfectly compatible with the behaviour of superconductors of the first type.

Abstract:
A quantum mechanical upper limit on the value of particle accelerations, or maximal acceleration (MA), is applied to compact stars. A few MA fermions are at most present in canonical white dwarfs and neutron stars. They drastically alter a star's stability conditions.

Abstract:
Fully covariant wave equations predict the existence of a class of inertial-gravitational effects that can be tested experimentally. In these equations inertia and gravity appear as external classical fields, but, by conforming to general relativity, provide very valuable information on how Einstein's views carry through in the world of the quantum.

Abstract:
A quantum mechanical upper limit on the value of particle accelerations is consistent with the behavior of a class of superconductors and well known particle decay rates. It also sets limits on the mass of the Higgs boson and affects the stability of compact stars. In particular, type-I superconductors in static conditions offer an example of a dynamics in which acceleration has an upper limit.

Abstract:
We generalize spin-rotation coupling to compound spin systems. In the case of muons bound to nuclei in a storage ring the decay process acquires a modulation. Typical frequencies for $Z/A\sim 1/2$ are $\sim 3\times 10^6$Hz, a factor 10 higher than the modulation observed in $g-2$ experiments.

Abstract:
Exact gauge structures arise in the evolution of spin-1/2 particles in conformally flat space-times. The corresponding Berry potentials can be Abelian or non-Abelian depending on the mass degeneracy of the system considered. Examples include de Sitter universes and maximal acceleration.

Abstract:
We show that recent, persistent discrepancies between theory and experiment can be interpreted as corrections to the gyro-gravitational ratio of the muon and lead to improved upper limits on the violation of discrete symmetries in rotational inertia.