Speaker
Description
The Magnus expansion provides an interesting alternative to the celebrated Dyson expansion in quantum field theory, and found early applications in quantum mechanics, atomic and molecular physics, and numerical solutions of matrix linear differential equations. Applications to field theory are more recent and are linked to the rewriting of the S-matrix as the exponential of the N-operator, namely S=exp(i N), which is particularly relevant in the computation of classical observables in general relativity.
I will describe direct methods to compute matrix elements of the N-operator, also called Magnus amplitudes, bypassing scattering amplitudes. At tree level, Magnus
amplitudes are expressed in terms of retarded and advanced propagators, with each diagram weighted by factors that we identify as Murua coefficients. At loop level
this structure is augmented by the Hadamard cut function, and we establish remarkable relations between loop and tree Magnus amplitudes via forward limits.
I describe this in the context of a scalar field theory, but our methods are applicable to general theories as well as to integral functions appearing in eg. gravitational-wave computations. Magnus amplitudes are manifestly free of hyper-classical terms, and combined with known relations between Magnus amplitudes and the
radial action, our results lay the groundwork for systematic and efficient calculations of classical observables from quantum field theory.