Outline BCS-BEC crossover theory and pair fluctuation theory a Gauge invariant linear response in bCs mean field theory: Consistent Fluctuation of Order parameter (CFOP a diagrammatic derivation of CFOP Gauge invariant linear response with pair fluctuation SummaryOutline ◼ BCS-BEC crossover theory and pair fluctuation theory ◼ Gauge invariant linear response in BCS mean field theory: Consistent Fluctuation of Order parameter (CFOP) ◼ A diagrammatic derivation of CFOP ◼ Gauge invariant linear response with pair fluctuation ◼ Summary