Analytic continuation of functional renormalization group equations

Abstract

Functional renormalization group equations are analytically continued from imaginary Matsubara frequencies to the real frequency axis. On the example of a scalar field with O(N ) symmetry we discuss the analytic structure of the flowing action and show how it is possible to derive and solve flow equations for real-time properties such as propagator residues and particle decay widths. The formalism conserves space-time symmetries such as Lorentz or Galilei invariance and allows for improved, self-consistent approximations in terms of derivative expansions in Minkowski space.

Local potential approximation for the renormalization group flow of fermionic field theories

“…In particular, one can also have Minkowskian spacetime signature. Then one can either use the Euclidean result with analytic continuation by applying an appropriate kernel for the suppression functional, which obeys the general analyticity requirements [24,25], or one can work directly in Minkowski space, where the formulation of the FRG equations is based on the 2-particle-irreducible methods [26,27]. Also, one should investigate Ansätze which imply nontrivial wave function renormalization (the next term of the gradient expansion).…”

Spectral functions for the quark-meson model phase diagram from the functional renormalization group

“…Such alternative approaches were proposed in [24][25][26] to involve an analytic continuation on the level of the flow equations themselves in order to provide correlation functions for timelike external momenta as the output of the calculations. In addition to its simplicity our approach enjoys a number of particular advantages: First of all, it is thermodynamically consistent in that the spacelike limit of zero external momentum in the 2-point correlation functions agrees with the curvature or screening masses as extracted from the thermodynamic grand potential [24].…”

Flow equations for spectral functions at finite external momenta

“…[8][9][10] and Ref. [11] for the functional renormalization group (FRG) and involve analytic continuations on the level of the flow equations. The FRG represents a powerful continuum framework for nonperturbative calculations particularly in quantum field theory and statistical physics; see Refs.…”