The Structure of the Magnus Expansion in QFT

The Magnus expansion provides an alternative series solution to the Schrödinger equation in terms of N, the log of the S-matrix. Unlike the usual time ordered exponential, the Magnus Expansion is in terms of nested commutators of Hamiltonians with a fixed temporal ordering. While it is known that matrix elements of the S-operator can be built out of Feynman propagators, we find that for the N-matrix another set of propagators is more natural. Working in phi cubed theory, we will investigate how this set of functions arises and uncover a surprising feature of loop-level "Magnus amplitudes".