  We examine the basic physics of type Ia supernova (SNe Ia) light curves with
a view toward interpreting the relations between peak luminosity, peak width,
and late-time slope in terms of the properties of the underlying explosion
models. We develop an analytic solution of the radiation transport problem in
the dynamic diffusion regime and show that it reproduces bolometric light
curves produced by more detailed calculations under the assumption of a
constant extinction coefficient. This model is used to derive the thermal
conditions in the interior of SNe Ia, to address the issue of time dependence
in the modeling of SNe Ia light curves and spectra and to show that these are
intrinsically time-dependent phenomena. The analytic model is then used to
study the sensitivity of light curves to various properties of supernova
explosions. We show that the dominant opacity arises from line transitions and
discuss the nature of line opacities in expanding media and the appropriateness
of various mean opacities used in light curve calculations.
