From conformal invariance towards dynamical symmetries of the collisionless Boltzmann equation

TL;DR

This paper explores how conformal invariance can be extended to include dynamical symmetries of the collisionless Boltzmann equation, especially under external forces, by developing new algebraic representations.

Contribution

It introduces novel conformal representations that incorporate external forces into the symmetry analysis of the Boltzmann equation.

Findings

Derived new symmetry representations for the Boltzmann equation with external forces.

Extended conformal symmetry to include particle momentum as an independent variable.

Outlined potential physical applications of the extended symmetries.

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.