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Cartan–Weyl Dirac and Laplacian Operators, Brownian Motions: The Quantum Potential and Scalar Curvature, Maxwell’s and Dirac-Hestenes Equations, and Supersymmetric Systems [Book Review]

Diego L. Rapoport

Foundations of Physics 35 (8):1383-1431 (2005)

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Quaternion Algebra on 4D Superfluid Quantum Space-Time: Gravitomagnetism.Valeriy I. Sbitnev - 2019 - Foundations of Physics 49 (2):107-143.details Gravitomagnetic equations result from applying quaternionic differential operators to the energy–momentum tensor. These equations are similar to the Maxwell’s EM equations. Both sets of the equations are isomorphic after changing orientation of either the gravitomagnetic orbital force or the magnetic induction. The gravitomagnetic equations turn out to be parent equations generating the following set of equations: the vorticity equation giving solutions of vortices with nonzero vortex cores and with infinite lifetime; the Hamilton–Jacobi equation loaded by the quantum potential. This equation (...) Download Export citation Bookmark 1 citation
Torsion Fields, Cartan–Weyl Space–Time and State-Space Quantum Geometries, their Brownian Motions, and the Time Variables.Diego L. Rapoport - 2007 - Foundations of Physics 37 (4-5):813-854.details We review the relation between spacetime geometries with trace-torsion fields, the so-called Riemann–Cartan–Weyl (RCW) geometries, and their associated Brownian motions. In this setting, the drift vector field is the metric conjugate of the trace-torsion one-form, and the laplacian defined by the RCW connection is the differential generator of the Brownian motions. We extend this to the state-space of non-relativistic quantum mechanics and discuss the relation between a non-canonical quantum RCW geometry in state-space associated with the gradient of the quantum-mechanical expectation (...) Download Export citation Bookmark 2 citations
Surmounting the Cartesian Cut Through Philosophy, Physics, Logic, Cybernetics, and Geometry: Self-reference, Torsion, the Klein Bottle, the Time Operator, Multivalued Logics and Quantum Mechanics. [REVIEW]Diego L. Rapoport - 2011 - Foundations of Physics 41 (1):33-76.details In this transdisciplinary article which stems from philosophical considerations (that depart from phenomenology—after Merleau-Ponty, Heidegger and Rosen—and Hegelian dialectics), we develop a conception based on topological (the Moebius surface and the Klein bottle) and geometrical considerations (based on torsion and non-orientability of manifolds), and multivalued logics which we develop into a unified world conception that surmounts the Cartesian cut and Aristotelian logic. The role of torsion appears in a self-referential construction of space and time, which will be further related to (...) Download Export citation Bookmark 3 citations
On Dark Energy, Weyl’s Geometry, Different Derivations of the Vacuum Energy Density and the Pioneer Anomaly.Carlos Castro - 2007 - Foundations of Physics 37 (3):366-409.details Two different derivations of the observed vacuum energy density are presented. One is based on a class of proper and novel generalizations of the de Sitter solutions in terms of a family of radial functions R that provides an explicit formula for the cosmological constant along with a natural explanation of the ultraviolet/infrared entanglement required to solve this problem. A nonvanishing value of the vacuum energy density of the order of ${10^{- 123} M_{\rm Planck}^4}$ is derived in agreement with the (...) Download Export citation Bookmark

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