Hidden symmetries of Eisenhart-Duval lift metrics and the Dirac equation with flux

Understand

The Eisenhart-Duval lift allows embedding non-relativistic theories into a Lorentzian geometrical setting.

• In this paper we study the lift from the point of view of the Dirac equation and its hidden symmetries.
• We show that dimensional reduction of the Dirac equation for the Eisenhart-Duval metric in general gives rise to the non-relativistic Levy-Leblond equation in lower dimension.
• We study in detail in which specific cases the lower dimensional limit is given by the Dirac equation, with scalar and vector flux, and the relation between lift, reduction and the hidden symmetries of the Dirac equation.