Introduction to Non-perturbative Renormalization Group for Out-of-Equilibrium Field Theories

  • Malo TarpinEmail author
Part of the Springer Theses book series (Springer Theses)


In this chapter, we present the framework of the NPRG applied to out-of-equilibrium field theories. In order to introduce out-of-equilibrium field theories, we first present in Sect. 3.2 the mapping from a SPDE with Gaussian noise to an action functional known as the MSRJD formalism. This allows us to discuss the specificities of out-of-equilibrium field theories, in particular the properties of causality of such field theories. Then in Sect. 3.3 we give a short presentation of the saddle-point method in statistical field theories as well as its shortfalls. This prepares and motivates the introduction of the NPRG in Sect. 3.4. Finally in Sect. 3.5 we spend some time on the treatment of causality in this setting. Prior to this, let us introduce some notations used throughout the manuscript.


  1. Amit DJ, Martin-Mayor V (2005) Field theory, the renormalization group, and critical phenomena, 3rd edn. WORLD SCIENTIFIC.
  2. Benitez F, Wschebor N (2013) Branching and annihilating random walks: exact results at low branching rate. Phys Rev E 87(5):052132. Scholar
  3. Berges J, Tetradis N, Wetterich C (2002) Non-perturbative renormalization flow in quantum field theory and statistical physics”. In: Physics Reports 363.4-6. Renormalization group theory in the new millennium. IV, pp. 223–386.
  4. Canet L, Chaté H, Delamotte B (2004) Quantitative phase diagrams of branching and annihilating randomwalks. Phys Rev Lett 92(25):255703. Scholar
  5. Canet L, Chaté H, Delamotte B (2011) General framework of the non-perturbative renormalization group for non-equilibrium steady states. J Phys A: Math Theor 44(49):495001. Scholar
  6. Canet L et al (2010) Nonperturbative renormalization group for the Kardar- Parisi-Zhang equation. Phys Rev Lett 104(15):150601. Scholar
  7. Cardy JL, Sugar RL (1980) Directed percolation and Reggeon field theory. J Phys A: Math Gen 13(12)L423.
  8. Delamotte B (2012) An introduction to the nonperturbative renormalization group. In: Schwenk A, Polonyi J (eds) Renormalization group and effective field theory approaches to many-body systems. Springer, Berlin, pp 49–132.
  9. Delamotte B, Tissier M, Wschebor N (2016) Scale invariance implies conformal invariance for the three-dimensional Ising model. Phys Rev E 93(1):012144. Scholar
  10. Duclut C, Delamotte B (2017) Frequency regulators for the nonperturbative renormalization group: a general study and the model A as a benchmark. Phys Rev E 95(1):012107. Scholar
  11. Ellwanger U (1994) Flow equations and BRS invariance for Yang-Mills theories. Phys Lett B 335:364. Scholar
  12. Gardiner CW (2009) Stochastic methods, 4th edn. Springer, BerlinzbMATHGoogle Scholar
  13. Gozzi E (1983) Functional integral approach to parisi-wu stochastic quantization: scalar theory. Phys Rev D 28:1922–1930. Scholar
  14. Landau LD (1937) On the theory of phase transitions. Zh Eksp Teor Fiz 7. [Ukr. J. Phys.53,25(2008)], pp. 19–32Google Scholar
  15. Le Bellac M (1998) Des phénomènes critiques aux champs de jauge (French Edition). EDP SCIENCESGoogle Scholar
  16. Morris TR (1994) The exact renormalisation group and approximate solutions. Int J Mod Phys A 9:2411. Scholar
  17. Polchinski J (1984) Renormalization and effective lagrangians. Nucl Phys B 231(2):269–295. Scholar
  18. Teodorovich E (1989) A hydrodynamic generalization of Ward’s identity. J Appl Math Mech 53(3):340–344. Scholar
  19. Touchette H (2014) Legendre-Fenchel transforms in a nutshellGoogle Scholar
  20. Täuber UC (2014) Critical dynamics: a field theory approach to equilibrium and non-equilibrium scaling behavior. Cambridge University Press, Cambridge.
  21. Wegner FJ, Houghton A (1973) Renormalization group equation for critical phenomena. Phys Rev A 8(1):401–412.
  22. Wetterich C (1993) Exact evolution equation for the effective potential. Phys Lett B 301(1):90–94.

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Authors and Affiliations

  1. 1.Institut für Theoretische Physik der Universität HeidelbergHeidelbergGermany

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