Translation-invariant quasi-free states for fermionic systems and the BCS approximation Bräunlich, Gerhard Hainzl, Christian Seiringer, Robert ; https://orcid.org/0000-0002-6781-0521 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 Publishing 2014 info:eu-repo/semantics/article doc-type:article text http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/1889 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> eng info:eu-repo/semantics/altIdentifier/doi/10.1142/S0129055X14500123 info:eu-repo/semantics/altIdentifier/wos/000341933500002 info:eu-repo/semantics/altIdentifier/arxiv/1305.5135 info:eu-repo/semantics/openAccess