We present a derivation of the transformation between the Q and U Stokes parameters and the E and B scalar and pseudo-scalar fields. We emphasize the geometrical properties that such transformation must satisfy. We present the E and B decomposition of some simple maps and of a model for a supernova remnant. We discuss the relative amplitudes of the E and B components and argue that for generic random maps E and B should have roughly the same amplitudes.
@article{arxiv.astro-ph/0106174,
title = {The nature of the E-B decomposition of CMB polarization},
author = {Matias Zaldarriaga},
journal= {arXiv preprint arXiv:astro-ph/0106174},
year = {2009}
}