Virtual Compton scattering off the nucleon at low energies
  We investigate the low-energy behavior of the four-point Green's function $\Gamma^{\mu\nu}$ describing virtual Compton scattering off the nucleon.   Using Lorentz invariance, gauge invariance, and crossing symmetry, we derive the leading terms of an expansion of the operator in the four-momenta $q$ and $q'$ of the initial and final photon, respectively.   The model-independent result is expressed in terms of the electromagnetic form factors of the free nucleon, i.e., on-shell information which one obtains from electron-nucleon scattering experiments.   Model-dependent terms appear in the operator at $O(q_\alpha q'_\beta)$, whereas the orders $O(q_\alpha q_\beta)$ and $O(q'_\alpha q'_\beta)$ are contained in the low-energy theorem for $\Gamma^{\mu\nu}$, i.e., no new parameters appear.   We discuss the leading terms of the matrix element and comment on the use of on-shell equivalent electromagnetic vertices in the calculation of ``Born terms'' for virtual Compton scattering. 
S. Scherer, A. Yu. Korchin, J. H. Koch