Analytic continuation of functional renormalization group equations

A bstractFunctional renormalization group equations are analytically continued from imaginary Matsubara frequencies to the real frequency axis. On the example of a scalar field with $ \mathcal{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.

[1]  M. Niedermaier,et al.  The Asymptotic Safety Scenario in Quantum Gravity , 2006, Living reviews in relativity.

[2]  C. Honerkamp,et al.  Alternative functional renormalization group approach to the single impurity Anderson model , 2012, 1210.0763.

[3]  Perturbation theory and non-perturbative renormalization flow in scalar field theory at finite temperature , 2006, hep-ph/0610004.

[4]  Janos Polonyi,et al.  Lectures on the functional renormalization group method , 2001, hep-th/0110026.

[5]  T. Gasenzer,et al.  Far-from-equilibrium quantum many-body dynamics , 2010, 1003.4163.

[6]  K. Wilson.  Renormalization Group and Critical Phenomena. I. Renormalization Group and the Kadanoff Scaling Picture , 1971 .

[7]  J. Braun.  Fermion interactions and universal behavior in strongly interacting theories , 2011, 1108.4449.

[8]  J. Blaizot,et al.  Calculation of the pressure of a hot scalar theory within the Non-Perturbative Renormalization Group , 2010, 1007.0991.

[9]  S. Coleman,et al.  Aspects of Symmetry , 1985 .

[10]  C. Wetterich,et al.  Exact evolution equation for the effective potential , 1993, 1710.05815.

[11]  Joseph Polchinski,et al.  Renormalization and effective lagrangians , 1984 .

[12]  D. Schuricht,et al.  Renormalization group analysis of the interacting resonant-level model at finite bias: Generic analytic study of static properties and quench dynamics , 2010, 1010.5666.

[13]  Bernd-Jochen Schaefer,et al.  Renormalization group approach towards the QCD phase diagram , 2006 .

[14]  Jan M. Pawlowski.  Aspects of the functional renormalisation group , 2007 .

[15]  S. Floerchinger.  Exact flow equation for bound states , 2010, 1001.4497.

[16]  T. Gasenzer,et al.  Towards far-from-equilibrium quantum field dynamics: A functional renormalisation-group approach , 2008 .

[17]  P. Kopietz,et al.  Spectral function and quasiparticle damping of interacting Bosons in two dimensions. , 2008, Physical review letters.

[18]  T. Pruschke,et al.  A finite-frequency functional renormalization group approach to the single impurity Anderson model , 2008, 0806.0246.

[19]  S. G. Jakobs,et al.  Nonequilibrium functional renormalization group with frequency-dependent vertex function: A study of the single-impurity Anderson model , 2009, 0911.5502.

[20]  L. Infeld.  Quantum Theory of Fields , 1949, Nature.

[21]  H. Gies,et al.  Functional renormalization for the Bardeen–Cooper–Schrieffer to Bose–Einstein condensation crossover , 2011, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[22]  S. Kehrein.  Scaling and decoherence in the nonequilibrium Kondo model. , 2004, Physical review letters.

[23]  Bertrand Delamotte,et al.  Nonperturbative renormalization-group study of reaction-diffusion processes. , 2004, Physical review letters.

[24]  Norman M. Dott.  An Introductory Review , 1962 .

[25]  Bertrand Delamotte,et al.  An Introduction to the Nonperturbative Renormalization Group , 2007, cond-mat/0702365.

[26]  Jean-Paul Blaizot,et al.  Nonperturbative renormalization group and momentum dependence of n-point functions. I. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[27]  Jean-Paul Blaizot,et al.  Nonperturbative renormalization group and momentum dependence of n-point functions. II. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[28]  Nonequilibrium functional renormalization group for interacting quantum systems. , 2007, Physical review letters.

[29]  D. Kennes,et al.  A renormalization group approach to time dependent transport through correlated quantum dots , 2011, 1111.6982.

[30]  Elements of the Continuous Renormalization Group , 1998, hep-th/9802039.

[31]  R. Schmidt,et al.  Excitation spectra and rf response near the polaron-to-molecule transition from the functional renormalization group , 2011, 1104.1379.

[32]  C. Karrasch,et al.  Functional renormalization group study of the interacting resonant level model in and out of equilibrium , 2009, 0911.5165.

[33]  C. Wetterich,et al.  Exact flow equation for composite operators , 2009, 0905.0915.

[34]  K. Aoki.  INTRODUCTION TO THE NON-PERTURBATIVE RENORMALIZATION GROUP AND ITS RECENT APPLICATIONS , 2000 .

[35]  Hugues Chaté,et al.  Quantitative phase diagrams of branching and annihilating random walks. , 2004, Physical review letters.

[36]  Functional renormalization group for nonequilibrium quantum many-body problems , 2006, cond-mat/0609457.

[37]  D. Schuricht,et al.  Relaxation versus decoherence: spin and current dynamics in the anisotropic Kondo model at finite bias and magnetic field. , 2009, Physical review letters.

[38]  Oliver J. Rosten.  Fundamentals of the Exact Renormalization Group , 2010, 1003.1366.

[39]  C. Bervillier,et al.  Exact renormalization group equations. An Introductory review , 2000 .

[40]  M. Salmhofer,et al.  Fermionic Renormalization Group Flows: Technique and Theory , 2001 .

[41]  F. Reininghaus,et al.  Real-time renormalization group in frequency space: A two-loop analysis of the nonequilibrium anisotropic Kondo model at finite magnetic field , 2009, 0902.1446.

[42]  Frank Saueressig,et al.  Asymptotically safe Lorentzian gravity. , 2011, Physical review letters.

[43]  N. Dupuis.  Infrared behavior and spectral function of a Bose superfluid at zero temperature , 2009, 0907.2779.

[44]  C. Wetterich,et al.  Non-perturbative renormalization flow in quantum field theory and statistical physics , 2002 .

[45]  K. Wilson.  The renormalization group and critical phenomena , 1983 .

[46]  A. Houghton,et al.  Renormalization group equation for critical phenomena , 1973 .

[47]  J. Berges,et al.  Nonthermal fixed points and the functional renormalization group , 2008, 0809.5208.

[48]  Nicolas Wschebor,et al.  A new method to solve the non-perturbative renormalization group equations , 2006 .

[49]  Holger Gies.  Introduction to the Functional RG and Applications to Gauge Theories , 2006 .

[50]  H. Gies,et al.  Functional renormalization for the BCS-BEC crossover , 2010, 1010.2890.

[51]  D. Litim.  Optimized renormalization group flows , 2001, hep-th/0103195.

[52]  F. Reininghaus,et al.  Erratum: Real-time renormalization group in frequency space: A two-loop analysis of the nonequilibrium anisotropic Kondo model at finite magnetic field [Phys. Rev. B 80, 045117 (2009)] , 2009 .

[53]  Miguel A Muñoz,et al.  Nonperturbative fixed point in a nonequilibrium phase transition. , 2005, Physical review letters.

[54]  Renormalization Flow of Bound States , 2001, hep-th/0107221.

[55]  M. Scully,et al.  The Quantum Theory of Light , 1974 .

[56]  S. Coleman.  Aspects of symmetry: Selected Erice lectures: Contents , 1985 .