  Considering the magnetic moment and polarizabilities of the nucleon we
emphasize the need for relativistic chiral EFT calculations. Our relativistic
calculations are done via the forward-Compton-scattering sum rules, thus
ensuring the correct analytic properties. The results obtained in this way are
equivalent to the usual loop calculations, provided no heavy-baryon expansion
or any other manipulations which lead to a different analytic structure (e.g.,
infrared regularization) are made. The Baldin sum rule can directly be applied
to calculate the sum of nucleon polarizabilities. In contrast, the GDH sum rule
is practically unsuitable for calculating the magnetic moments. The
breakthrough is achieved by taking the derivatives of the sum rule with respect
to the anomalous magnetic moment. As an example, we apply the derivative of the
GDH sum rule to the calculation of the magnetic moment in QED and reproduce the
famous Schwinger's correction from a tree-level cross-section calcualation. As
far as the nucleon properties are concerned, we focus on two issues: 1) chiral
behavior of the nucleon magnetic moment and 2) reconciliation of the chiral
loop and $\Delta$-resonance contributions to the nucleon magnetic
polarizability.
