Teleparallelism, Brownian Motion, Quantum Mechanics and Fluid-Dynamics I

Details Teleparallelism, Brownian Motion, Quantum Mechanics and Fluid-Dynamics I Teleparallelism, Brownian Motion, Quantum Mechanics and Fluid-Dynamics I

Dec 2002

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2002nmgm.meet.1096r&link_type=abstract

"THE NINTH MARCEL GROSSMANN MEETING On Recent Developments in Theoretical and Experimental General Relativity, Gravitation and R

Physics

Scientific paper

Extending the rules of teleparallelism for the introduction of a metric and a connection with torsion on a smooth manifold, M, we define generalized Brownian motions on M starting with a standard Wiener process. The laplacian operator generating this diffusion is the square of the teleparallelism connection on M, yet it is found to depend on the trace-torsion, and thus we restrict to Riemann-Cartan-Weyl connections. We extend these constructions to the generalized Brownian motions of differential forms. We apply this to give random covariant implicit solutions of the Navier-Stokes equations. We give the constitutive equations for the trace-torsion Q, and obtain a non-linear wave equation with quantum potential term for a scalar ψ appearing in the term d lnψ of Q. We relate the diffusion with drift ∇lnψ, to the heat kernel of quantum gravity for a scalar field. In Q appear two electromagnetic potentials which are proved to produce the time-evolution irreversibility of the Brownian motions. They appear related to the rotational degrees of freedom of a massive non-linear Dirac-Hestenes spinor field which defines a global spinor structure on M and a solution of the Clifford-Maxwell equation.

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