The problem of determining the effects of the surrounding plasma on nuclear
reaction rates in stars is formulated ab initio, using the techniques of
quantum statistical mechanics. We derive a result that expresses the complete
effects of Coulomb barrier penetration and of the influence of the surrounding
plasma in terms of matrix elements of well defined operators. We find that
possible "dynamical screening" effects that have been discussed in the
literature are absent. The form of our results suggests that an approach that
relies on numerical calculations of the correlation functions in a classical
Coulomb gas, followed by construction of an effective two body potential and a
quantum barrier penetration calculation, will miss physics that is as important
as the physics that it includes.Comment: 66 pages, revtex, Errors Fixed, Explanation Adde