Koopman wavefunctions and Clebsch variables in Vlasov-Maxwell kinetic theory

Abstract

Motivated by recent discussions on the possible role of quantum computation in plasma simulations, here, we present different approaches to Koopman’s Hilbert-space formulation of classical mechanics in the context of Vlasov-Maxwell kinetic theory. The celebrated Koopman-von Neumann construction is provided with two different Hamiltonian structures: one is canonical and recovers the usual Clebsch representation of the Vlasov density, the other is non-canonical and appears to overcome certain issues emerging in the canonical formalism. Furthermore, the canonical structure is restored for a variant of the Koopman-von Neumann construction that carries a different phase dynamics. Going back to van Hove’s prequantum theory, the corresponding Koopman-van Hove equation provides an alternative Clebsch representation which is then coupled to the electromagnetic fields. Finally, the role of gauge transformations in the new context is discussed in detail.