respectively. The symbol W (q, R, t) indicates the phase of the photon-nuclear wavefunction χ(q, R,t), has the dimensions of an action and is related to the gauge phase θ (q, R,t) introduced above. In this work, the gauge for the quantum dynamics calculations will be chosen such that the photon-nuclear wavefunction is always non-negative and real, namely χ(q, R,t) = + dr|Ψ(r, q, R,t)| 2 , meaning that W (q, R, t) = 0. In this particular gauge, Eqs. (18) and (19) show that the TDVP becomes the nuclear and the photonic momentum fields, respectively.