The Renormalization Group: Fundamental Aspects

  • Lothar Schäfer


This chapter is of central importance. We introduce here the renormalization group, based on the observation that our choice of the elementary segment involves a large amount of arbitrariness. Thus there should exist a mapping from segments of size ℓ = ℓ0 to segments of size ℓ1 which does not change macroscopic observables. It also should not affect the basic structure of the model, viz. Gaussian segments interacting via some local two-body repulsion. Our previous arguments on the structure of the model never refered to any distinguished value of ℓ. In Sect. 8.1 we formulate these considerations more precisely in terms of the ‘Renormalization Group Hypothesis’. This is to be amended by the ‘Fixed Point Hypothesis’, assuming that with increasing size of the elementary segment the excluded volume constant tends to some finite limiting value. Universal scaling and power laws follow naturally.


Renormalization Group Flow Equation Cluster Expansion Elementary Segment Point Hypothesis 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Lothar Schäfer
    • 1
  1. 1.FB7 PhysikUniversität GH EssenEssenGermany

Personalised recommendations