Koopman wavefunctions and Clebsch variables in Vlasov–Maxwell kinetic theory

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 classical mechanics context Vlasov-Maxwell kinetic theory. The celebrated Koopman-von Neumann construction is provided with two Hamiltonian structures: one canonical and recovers usual Clebsch representation Vlasov density, other noncanonical appears overcome certain issues emerging formalism. Furthermore, structure restored for a variant that carries phase dynamics. Going back van Hove's prequantum theory, corresponding Koopman-van Hove equation provides an alternative which then coupled electromagnetic fields. Finally, gauge transformations new discussed detail.