Vlasov equation and collisionless hydrodynamics adapted to curved spacetime (original) (raw)

The quantum hydrodynamic representation in curved space

2017

The work shows that the evolution of quantum states in the hydrodynamic representation can be obtained by Lagrangean motion equations that can be derived by a minimum action principle. The quantum behavior introduces an extra-action term that is the direct consequence of the quantization condition. The Lagrangean density in the non-Euclidean space-time has been obtained by using the physics covariance postulate. The description in curved space is obtained by minimizing the overall action comprehending the variation due to the metric tensor. The energy impulse tensor density for a scalar uncharged particle as well as of a fermion have been derived.

The quantum hydrodynamic representation in curved space and the related Einstein equation

2017

The work shows that the evolution of quantum states in the hydrodynamic representation can be obtained by Lagrangean motion equations that can be derived by a minimum action principle. Once the quantum hydrodynamic motion equations have been generalized in the non-Euclidean space-time by using the physics covariance postulate, the quantum gravity equation, determining the geometry of the space-time necessary to give full meaning to them, is obtained by minimizing the overall action comprehending the gravitational field. The theoretical output for a scalar uncharged field shows the spontaneous emergence of a cosmological energy impulse tensor density (CEITD) that in the classical limit converges to a constant. The mean value of CEITD in the galactic space leads to the correct order of magnitude of the cosmological constant. The coupling of the quantum gravitational equation with half-spin fermions is finally developed.

80 83 v 1 2 6 A ug 2 00 3 Field-Particle Dynamics in Spacetime Geometries

2003

With the aid of a Fermi-Walker chart associated with an orthonormal frame attached to a time-like curve in spacetime, a discussion is given of relativistic balance laws that may be used to construct models of massive particles with spin, electric charge and a magnetic moment, interacting with background electromagnetic fields and gravitation described by non-Riemannian geometries. A natural generalisation to relativistic Cosserat media is immediate.