Hi there, I'm working on getting a presentation together for a graduate course I'm taking and chose to give a brief introduction on spin polarizabilities. In the case of the nucleon, these 4 intrinsic quantities manifest themselves in a 3rd-order expansion of the Compton Scattering Hamiltonian, as seen on page 12 of arXiv:hep-ph/9910427v2 26 Oct 1999 (http://arxiv.org/pdf/hep-ph/9910427). I've tried to recreate this equation from scratch but honestly have no clue how this expansion came to play...is it some sort of Taylor Series term? I have little experience in multivariable expansions. If anyone could provide some guidance on this, I would be very grateful.