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arXiv · 1308.1238

Velocity-Field Theory, Boltzmann's Transport Equation and Geometry

Shoichi Ichinose
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Abstract

Boltzmann equation describes the time development of the velocity distribution in the continuum fluid matter. We formulate the equation using the field theory where the {\it velocity-field} plays the central role. The matter (constituent particles) fields appear as the density and the viscosity. {\it Fluctuation} is examined, and is clearly discriminated from the quantum effect. The time variable is {\it emergently} introduced through the computational process step. The collision term, for the (velocity)**4 potential (4-body interaction), is explicitly obtained and the (statistical) fluctuation is closely explained. The present field theory model does {\it not} conserve energy and is an open-system model. (One dimensional) Navier-Stokes equation or Burger's equation, appears. In the latter part, we present a way to directly define the distribution function by use of the geometry, appearing in the mechanical dynamics, and Feynman's path-integral.

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Shoichi Ichinose. 2013-10-09. Velocity-Field Theory, Boltzmann's Transport Equation and Geometry. https://arxiv.org/abs/1308.1238

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