  We develop the formalism necessary to study four-point functions of the
cosmic microwave background (CMB) temperature and polarization fields. We
determine the general form of CMB trispectra, with the constraints imposed by
the assumption of statistical isotropy of the CMB fields, and derive
expressions for their estimators, as well as their Gaussian noise properties.
We apply these techniques to initial non-Gaussianity of a form motivated by
inflationary models. Due to the large number of four-point configurations, the
sensitivity of the trispectra to initial non-Gaussianity approaches that of the
temperature bispectrum at high multipole moment. These trispectra techniques
will also be useful in the study of secondary anisotropies induced for example
by the gravitational lensing of the CMB by the large scale structure of the
universe.
