 for \(Q(t)\), the simplest first-order evolution equation for the positions of the particles that is compatible with the Galilean (and time-reversal) covariance of the Schrödinger evolution (Dürr, Goldstein, &amp; Zanghì 1992a: 852–854). Here \(\hslash\) is Planck’s constant divided by \(2\pi\), m\(_k\) is the mass of the \(k\)-th particle, and \(\partial_k = (\partial /\partial x_k,\partial /\partial y_k,\partial /\partial z_k)\) is the gradient with respect to the generic coordinates \(\boldsymbol{q}_k = (x_k,y_k,z_k)\) of the \(k\)-th particle. If \(\psi\) is spinor-valued, the two products involving \(\psi\) in the equation should be understood as scalar products (involving sums of products of spinor components). When external magnetic fields are present, the gradient should be understood as the covariant derivative, involving the vector potential. (Since the denominator on the right hand side of the guiding equation vanishes at the nodes of \(\psi\), global existence and uniqueness for the Bohmian dynamics is a nontrivial matter. It is proven in Berndl, Dürr, et al. 1995 and in Teufel and Tumulka 2005.) 