I summarize Density Functional Theory (DFT) in a language familiar to quantum field theorists, and introduce several apparently novel ideas for constructing {it systematic} approximations for the density functional. I also note that, at least within
the large $K$ approximation ($K$ is the number of electron spin components), it is easier to compute the quantum effective action of the Coulomb photon field, which is related to the density functional by algebraic manipulations in momentum space.
Recent observations of the transiting super-Earth GJ 1214b reveal that its atmosphere may be hydrogen-rich or water-rich in nature, with clouds or hazes potentially affecting its transmission spectrum in the optical and very-near-IR. Here we further
examine the possibility that GJ 1214b does indeed possess a hydrogen-dominated atmosphere, which is the hypothesis that is favored by models of the bulk composition of the planet. We study the effects of non-equilibrium chemistry (photochemistry, thermal chemistry, and mixing) on the planets transmission spectrum. We furthermore examine the possibility that clouds could play a significant role in attenuating GJ 1214bs transmission spectrum at short wavelengths. We find that non-equilibrium chemistry can have a large effect on the overall chemical composition of GJ 1214bs atmosphere, however these changes mostly take place above the height in the atmosphere that is probed by transmission spectroscopy. The effects of non-equilibrium chemistry on GJ 1214bs transmission spectrum are therefore minimal, with the largest effects taking place if the planets atmosphere has super-solar metallicity and a low rate of vertical mixing. Interestingly, we find that the best fit to the observations of GJ 1214bs atmosphere in transmission occur if the planets atmosphere is deficient in CH4, and possesses a cloud layer at a pressure of ~200 mbar. This is consistent with a picture of efficient methane photolysis, accompanied by formation of organic haze that obscures the lower atmosphere of GJ 1214b at optical wavelengths. However, for methane to be absent from GJ 1214bs transmission spectrum, UV photolysis of this molecule must be efficient at pressures of greater than ~1 mbar, whereas we find that methane only photolyzes to pressures less than 0.1 mbar, even under the most optimistic assumptions. (Abridged)
