Gauge invariance, locality, and theσ−2photoabsorption sum rule

Abstract

The requirements of gauge invariance for the photoabsorption and Compton amplitudes are used to evaluate the ${\sigma }_{-2\mathrm{}}$ sum rule through terms of order (1/mass). This expression is shown to equal the derivative of the dispersive part of the forward Compton amplitude with respect to the squared photon energy. In the absence of "frozen" meson degrees of freedom this is equivalent to the derivative of the entire Compton amplitude. If static exchange currents or finite nucleon charge distributions are present, the seagull terms of our model are nonlocal and modify the sum rule.