Normally Ordered Disentanglement of Multi-Dimensional Schrödinger Algebra Exponentials

We derive a normally ordered disentanglement or splitting formula for exponentials of the infinite-dimensional Schrödinger Lie algebra generators. As an application we compute the vacuum characteristic function of a quantum random variable defined as a self-adjoint finite sum of Fock space operators, satisfying the multi-dimensional Schrödinger Lie algebra commutation relations.