From conformal invariance towards dynamical symmetries of the collisionless Boltzmann equation

Abstract

Dynamical symmetries of the collisionless Boltzmann transport equation, or Vlasov equation, but under the influence of an external driving force, are derived from non-standard representations of the $2D$ conformal algebra. In the case without external forces, the symmetry of the conformally invariant transport equation is first generalised by considering the particle momentum as an independent variables. This new conformal representation can be further extended to include an external force. The construction and possible physical applications are outlined.

Latex2e, 18 pages, no figures

References in corpus (3)

• Non-relativistic conformal symmetries and Newton-Cartan structures
• On nonlinear partial differential equations with an infinite-dimensional conditional symmetry
• Vlasov equation and $N$-body dynamics - How central is particle dynamics to our understanding of plasmas?

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