Virtual Compton Scattering and Generalized Polarizabilities of the Proton

Threshold photon electroproduction off the proton allows one to measure new electromagnetic observables which generalise the usual polarisabilities. There are -- a priori -- ten "generalised polarisabilities", functions of the virtual photon mass. The purpose of this paper is to lay down the appropriate formalism to extract these quantities from the photon electroproduction cross sections. We also give a first estimate of the generalised polarisabilities in the non relativistic quark model.