Exact scheme independence at one loop

The requirement that the quantum partition function be invariant under a renormalization group transformation results in a wide class of exact renormalization group equations, differing in the form of the kernel. Physical quantities should not be sensitive to the particular choice of the kernel. We demonstrate this scheme independence in four dimensional scalar field theory by showing that, even with a general kernel, the one-loop beta function may be expressed only in terms of the effective action vertices, and thus, under very general conditions, the universal result is recovered.