Title: How to generalize the Magnus expansion for unbounded operators?

 Abstract: The Magnus series is a general solution for the Schrödinger equation that competes with the familiar solution known as the Dyson series. We discuss under which mathematical conditions these expansions are in-equivalent, and show that this happens when dealing with unbounded Hamiltonians. Then, we provide an alternative construction that is manifestly unitary, regardless of the choice of the Hamiltonian, and study various aspects of the implications. The new construction involves an additional self-adjoint operator that might evolve in a non-gradual way. Its corresponding dynamics exhibit the behavior of a collective object governed by a singular Liouville's equation that performs transitions at a measure 0 set. 

Based on https://arxiv.org/abs/2402.18499