derived by Christof Wetterich and Tim R. Morris in 1993. Here ∂ ∂ k denotes a derivative with respect to the RG scale k at fixed values of the fields. Furthermore, Γ Γ k ( 1 , 1 ) denotes the functional derivative of Γ Γ k from the left-hand-side and the right-hand-side respectively, due to the tensor structure of the equation. This feature is often shown simplified by the second derivative of the effective action. The functional differential equation for Γ Γ k must be supplemented with the initial condition Γ Γ k → → Λ Λ = S , where the "classical action" S describes the physics at the microscopic ultraviolet scale k = Λ Λ . Importantly, in the infrared limit k → → 0 the full effective action Γ Γ = Γ Γ k → → 0 is obtained. In the Wetterich equation STr denotes a supertrace which sums over momenta, frequencies, internal indices, and fields (taking bosons with a plus and fermions with a minus sign). The exact flow equation for Γ Γ k has a one-loop structure. This is an important simplification compared to perturbation theory, where multi-loop diagrams must be included. The second functional derivative Γ Γ k ( 2 ) = Γ Γ k ( 1 , 1 ) is the full inverse field propagator modified by the presence of the regulator R k .