  We present a projector formalism which allows to define dynamical
polarizabilities of the nucleon from a multipole expansion of the nucleon
Compton amplitudes. We give predictions for the energy dependence of these
dynamical polarizabilities both from dispersion theory and from
leading-one-loop chiral effective field theory. Based on the good agreement
between the two theoretical frameworks, we conclude that the energy dependence
of the dynamical polarizabilities is dominated by chiral dynamics, except in
those multipole channels where the first nucleon resonance Delta(1232) can be
excited. Both the dispersion theory framework and a chiral effective field
theory with explicit Delta(1232) degrees of freedom lead to a very good
description of the available low energy proton Compton data. We discuss the
sensitivity of the proton Compton cross section to dynamical polarizabilities
of different multipole content and present a fit of the static electric and
magnetic dipole polarizabilities from low-energy Compton data up to omega=170
MeV, finding alpha_E=(11.04+-1.36)*10^(-4) fm^3, beta_M =(2.76-+1.36)*10^(-4)
fm^3.
