9870597 Belitz This is a theoretical research grant with the objective to enhance current understanding of many-electron systems at very low temperatures, and especially of phase transitions and other collective phenomena in these systems. A particular objective of the research is to further develop and apply an effective field theory that allows a systematic treatment of electronic systems in the presence of impurities. The methods employed include general field theoretic techniques, the renormalization group, and many- body perturbation theory. Specific systems for which this work is relevant include magnets with impurities, superconductors, and doped semiconductors. %%% This is a theoretical research grant with the objective to enhance current understanding of many-electron systems at very low temperatures, and especially of phase transitions and other collective phenomena in these systems. A particular objective of the research is to further develop and apply an effective field theory that allows a systematic treatment of electronic systems in the presence of impurities. The methods employed include general field theoretic techniques, the renormalization group, and many- body perturbation theory. Specific systems for which this work is relevant include magnets with impurities, superconductors, and doped semiconductors. ***