Feynman-Hellmann approach to transition matrix elements

The Feynman-Hellmann approach to computing matrix elements in lattice QCD by first adding a perturbing operator to the action is described using the transition matrix and the Dyson expansion formalism. This perturbs the energies in the two-point baryon correlation function, from which the matrix element can be obtained. In particular at leading order in the perturbation we need to diagonalize a matrix of near-degenerate energies. While the method is general for all hadrons, we apply it here to a study of a sigma to nucleon baryon transition vector matrix element.