Differential and Integral Invariance of the Relativistic Vlasov-Boltzmann Equation and the Associated Invariant Variational Problem
Burlet, Daniel John
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https://hdl.handle.net/2142/72450
Description
Title
Differential and Integral Invariance of the Relativistic Vlasov-Boltzmann Equation and the Associated Invariant Variational Problem
Author(s)
Burlet, Daniel John
Issue Date
1993
Doctoral Committee Chair(s)
Axford, Roy A.
Department of Study
Nuclear Engineering
Discipline
Nuclear Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Engineering, Nuclear
Physics, Fluid and Plasma
Physics, Elementary Particles and High Energy
Abstract
Relativistic Vlasov-Boltzmann kinetic equations are constructed from quantum field theory for scalar bosons and Dirac fermion fields. Lie's principle of differential invariance is extended to the case of non-linear integro-differential equations for both scalar and matrix distribution functions, corresponding to scalar and fermion kinetic equations respectively, and then is used to demonstrate the invariance of these equations under the action of the Poincare group. The invariant variational problem is then constructed for these equations, and is shown to yield the kinetic equations as Euler-Lagrange equations for the variational principle, as well as first integrals for the Euler-Lagrange, which are interpreted as conservation laws, for energy-linear momentum and angular momentum under the action of the Poincare group. Finally, macroscopic balance equations for particle and energy density, linear and angular momentum, and entropy production, appropriate for the description of non-ideal relativistic magnetohydrodynamics are obtained from moments of the relativistic kinetic equation.
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