Renormalization group flow for SU(2) Yang-Mills theory and gauge invariance

Oct, 1993
27 pages
Published in:
  • Nucl.Phys.B 421 (1994) 429-455
e-Print:
Report number:
  • UPRF-93-388

Citations per year

19942001200820152022051015
Abstract: (desy)
We study the formulation of the Wilson renormalization group (RG) method for a non-Abelian gauge theory. We analyze the simple case of SU(2)SU(2) in which the Lagrangian at the ultraviolet cutoff \L_0 contains nine relevant couplings, \ie parameters with non-negative dimension, while the classical theory contains only one coupling gg. We show that both the physical parameter, \ie the coupling gg at the subtraction point μ\mu, and the local gauge symmetry can be implemented by suitable boundary conditions for the RG flow. This procedure is similar to the one we used for QED with two crucial new points: the non-linearity of the Slavnov-Taylor (ST) identities and the presence of two couplings with non-negative dimension absent at tree level. To show the practical character of this formulation we deduce the perturbative expansion for the vertex functions in terms of the physical coupling gg at the subtraction point μ\mu and perform one loop calculations. In particular we analyze to this order some ST identities. We give a schematic proof of perturbative renormalizability.
  • gauge field theory: SU(2)
  • gauge field theory: Yang-Mills
  • renormalization group: beta function
  • effective action
  • perturbation theory: higher-order
  • integral equations
  • boundary condition