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A previous paper~\cite{Bern:2022kto} identified a puzzle stemming from theamplitudes-based approach to spinning bodies in general relativity: additionalWilson coefficients appear compared to current worldline approaches toconservative dynamics of generic astrophysical objects, including neutronstars. In this paper we clarify the nature of analogous Wilson coefficients inthe simpler theory of electrodynamics. We analyze the original field-theoryconstruction, identifying definite-spin states some of which have negativenorms, and relating the additional Wilson coefficients in the classical theoryto transitions between different quantum spin states. We produce a new versionof the theory which also has additional Wilson coefficients, but nonegative-norm states. We match, through $\mathcal O(\alpha^2)$ and $\mathcalO(S^2)$, the Compton amplitudes of these field theories with those of amodified worldline theory with extra degrees of freedom introduced by releasingthe spin supplementary condition. We build an effective two-body Hamiltonianthat matches the impulse and spin kick of the modified field theory and of theworldline theory, displaying additional Wilson coefficients compared tostandard worldline approaches. The results are then compactly expressed interms of an eikonal formula. Our key conclusion is that, contrary to standardapproaches, while the magnitude of the spin tensor is still conserved, themagnitude of the spin vector can change under conserved Hamiltonian dynamicsand this change is governed by the additional Wilson coefficients. For specificvalues of Wilson coefficients the results are equivalent to those from adefinite spin obeying the spin supplementary condition, but for generic valuesthey are physically inequivalent. These results warrant detailed studies of thecorresponding issues in general relativity.

Quantum Field Theory, Worldline Theory, and Spin Magnitude Change in Orbital Evolution