article published yes Gerhard Bräunlich author Christian Hainzl author Robert Seiringer author 4AFD0470-F248-11E8-B48F-1D18A9856A870000-0002-6781-0521 RoSe department We study translation-invariant quasi-free states for a system of fermions with two-particle interactions. The associated energy functional is similar to the BCS functional but also includes direct and exchange energies. We show that for suitable short-range interactions, these latter terms only lead to a renormalization of the chemical potential, with the usual properties of the BCS functional left unchanged. Our analysis thus represents a rigorous justification of part of the BCS approximation. We give bounds on the critical temperature below which the system displays superfluidity. World Scientific Publishing2014 eng 1305.5135 00034193350000210.1142/S0129055X14500123 267 Bräunlich G, Hainzl C, Seiringer R. Translation-invariant quasi-free states for fermionic systems and the BCS approximation. <i>Reviews in Mathematical Physics</i>. 2014;26(7). doi:<a href="https://doi.org/10.1142/S0129055X14500123">10.1142/S0129055X14500123</a> Bräunlich, G., Hainzl, C., &#38; Seiringer, R. (2014). Translation-invariant quasi-free states for fermionic systems and the BCS approximation. <i>Reviews in Mathematical Physics</i>. World Scientific Publishing. <a href="https://doi.org/10.1142/S0129055X14500123">https://doi.org/10.1142/S0129055X14500123</a> G. Bräunlich, C. Hainzl, R. Seiringer, Reviews in Mathematical Physics 26 (2014). Bräunlich G, Hainzl C, Seiringer R. 2014. Translation-invariant quasi-free states for fermionic systems and the BCS approximation. Reviews in Mathematical Physics. 26(7), 1450012. G. Bräunlich, C. Hainzl, and R. Seiringer, “Translation-invariant quasi-free states for fermionic systems and the BCS approximation,” <i>Reviews in Mathematical Physics</i>, vol. 26, no. 7. World Scientific Publishing, 2014. Bräunlich, Gerhard, Christian Hainzl, and Robert Seiringer. “Translation-Invariant Quasi-Free States for Fermionic Systems and the BCS Approximation.” <i>Reviews in Mathematical Physics</i>. World Scientific Publishing, 2014. <a href="https://doi.org/10.1142/S0129055X14500123">https://doi.org/10.1142/S0129055X14500123</a>. Bräunlich, Gerhard, et al. “Translation-Invariant Quasi-Free States for Fermionic Systems and the BCS Approximation.” <i>Reviews in Mathematical Physics</i>, vol. 26, no. 7, 1450012, World Scientific Publishing, 2014, doi:<a href="https://doi.org/10.1142/S0129055X14500123">10.1142/S0129055X14500123</a>. 18892018-12-11T11:54:33Z2025-09-29T13:07:59Z