Von Neumann's Quantization of General Relativity

Von Neumann's procedure is applied for quantization of General Relativity. We quantize the initial data of dynamical variables at the Planck epoch, where the Hubble parameter coincides with the Planck mass. These initial data are defined via the Fock simplex in the tangent Minkowskian space-time and the Dirac conformal interval. The Einstein cosmological principle is applied for the average of the spatial metric determinant logarithm over the spatial volume of the visible Universe. We derive the splitting of the general coordinate transformations into the diffeomorphisms (as the object of the second N\"other theorem) and the initial data transformations (as objects of the first N\"other theorem). Following von Neumann, we suppose that the vacuum state is a quantum ensemble. The vacuum state is degenerated with respect to quantum numbers of non-vacuum states with the distribution function that yields the Casimir effect in gravidynamics in analogy to the one in electrodynamics. The generation functional of the perturbation theory in gravidynamics is given as a solution of the quantum energy constraint. We discuss the region of applicability of gravidynamics and its possible predictions for explanation of the modern observational and experimental data.Comment: 14 pages, updated version with extended discussio

3-Ketosphinganine provokes the accumulation of dihydroshingolipids and induces autophagy in cancer cells.

Although several reports describe the metabolic fate of sphingoid bases and their analogs, as well as their action and that of their phosphates as regulators of sphingolipid metabolizing-enzymes, similar studies for 3-ketosphinganine (KSa), the product of the first committed step in de novo sphingolipid biosynthesis, have not been reported. In this article we show that 3-ketosphinganine (KSa) and its dideuterated analog at C4 (d2KSa) are metabolized to produce high levels of dihydrosphingolipids in HGC27, T98G and U87MG cancer cells. In contrast, either direct C1 O-phosphorylation or N-acylation of d2KSa to produce dideuterated ketodihydrosphingolipids does not occur. We also show that cells respond to d2KSa treatment with induction of autophagy. Time-course experiments agree with sphinganine, sphinganine 1-phosphate and dihydroceramides being the mediators of autophagy stimulated by d2KSa. Enzyme inhibition studies support that inhibition of Des1 by 3-ketobases is caused by their dihydroceramide metabolites. However, this effect contributes to increasing dihydrosphingolipid levels only at short incubation times, since cells respond to long time exposure to 3-ketobases with Des1 overexpression. The translation of these overall effects into cell fate is discussed.Partial financial support from the ‘‘Ministerio de Ciencia e Innovación’’, Spain (Grants SAF2011-22444), ‘‘Ministerio de Economía y Competitividad’’ (CTQ2014-54743-R), CSIC (Grant PIE 2008801034) and Fundacio´ La Marato´ TV3 (Grant 112130 and 112132) is acknowledged. A PhD fellowship from SENESCYTEcuador to Y. F. O. is also acknowledged. We thank Pedro Rayo for his excellent technical assistance.Peer reviewe

Rotation and twist regular modes for trapped ghosts

A parameter-independent notion of stationary slow motion is formulated then applied to the case of stationary rotation of massless trapped ghosts. The excitations correspond to a rotation mode with angular momentum $J\neq 0$ and twist modes. It is found that the rotation mode, which has no parity, causes excess in the angular velocity of dragged distant coordinate frames in one sheet of the wormhole while in the other sheet the angular velocity of the ghosts is that of rotating stars: $2J/r^3$. As to the twist modes, which all have parity, they cause excess in the angular velocity of one of the throat's poles with respect to the other.Comment: 11 pages, 3 figures; General Relativity and Gravitation - 201

Non-compact Groups, Coherent States, Relativistic Wave Equations and the Harmonic Oscillator II: Physical and Geometrical Considerations

The physical meaning of the particularly simple non-degenerate supermetric, introduced in the previous part by the authors, is elucidated and the possible connection with processes of topological origin in high energy physics is analyzed and discussed. New possible mechanism of the localization of the fields in a particular sector of the supermanifold is proposed and the similarity and differences with a 5-dimensional warped model are shown. The relation with gauge theories of supergravity based in the $OSP(1/4)$ group is explicitly given and the possible original action is presented. We also show that in this non-degenerate super-model the physic states, in contrast with the basic states, are observables and can be interpreted as tomographic projections or generalized representations of operators belonging to the metaplectic group $Mp(2)$. The advantage of geometrical formulations based on non-degenerate super-manifolds over degenerate ones is pointed out and the description and the analysis of some interesting aspects of the simplest Riemannian superspaces are presented from the point of view of the possible vacuum solutions.Comment: Stile of the text improved in Journa