Functional renormalization group with a compactly supported smooth regulator function

Abstract

The functional renormalization group equation with a compactly supported smooth (CSS) regulator function is considered. It is demonstrated that in an appropriate limit the CSS regulator recovers the optimized one and it has derivatives of all orders. The more generalized form of the CSS regulator is shown to reduce to all major type of regulator functions (exponential, power-law) in appropriate limits. The CSS regulator function is tested by studying the critical behavior of the bosonized two-dimensional quantum electrodynamics in the local potential approximation and the sine-Gordon scalar theory for d < 2 dimensions beyond the local potential approximation. It is shown that a similar smoothing problem in nuclear physics has already been solved by introducing the so called Salamon-Vertse potential which can be related to the CSS regulator.

Truncation effects in the functional renormalization group study of spontaneous symmetry breaking

“…R k is a properly chosen infrared (IR) regulator function which fulfills a few basic constraints to ensure that Γ k approaches the bare action in the UV limit (k → Λ) and the full quantum effective action in the IR limit (k → 0): details are reported in appendix A, where we also discuss the more commonly used regulators for O(N ) model and a more general choice able to recover all major types of regulators used in literature [46]. Since RG equations are functional partial differential equations, it is not possible to solve them in general and approximations are required.…”

“…Various types of regulator functions can be chosen, but a more general choice is the so called CSS regulator [46] which recovers all major types of regulators in its appropriate limits. By using a particular normalization [64,65] it has the following form …”

Strictly finite-range potential for light and heavy nuclei

“…A drawback is, however, that it is not analytic because at ρ 0 the Taylor series is not equal to the function. Nevertheless, it has turned out to be useful in quantum electrodynamics, too, as a compactly supported smooth regulator function [6].…”

Harmonic expansion of the effective potential in a functional renormalization group at finite chemical potential

“…There are different formulation for the exact functional equation that forms the basis of FRG computations, in this paper we will use Wetterich equation [8,9]. One can also use different regulators [10], here we use Litim's regulator [11]. The Wetterich equation is exact, but is valid in infinite dimensional operator space.…”