2 research outputs found
Renormalization group flow for SU(2) Yang-Mills theory and gauge invariance
We study the formulation of the Wilson renormalization group (RG) method for
a non-Abelian gauge theory. We analyze the simple case of and show that
the local gauge symmetry can be implemented by suitable boundary conditions for
the RG flow. Namely we require that the relevant couplings present in the
physical effective action, \ie the coefficients of the field monomials with
dimension not larger than four, are fixed to satisfy the Slavnov-Taylor
identities. The full action obtained from the RG equation should then satisfy
the same identities. This procedure is similar to the one we used in QED. In
this way we avoid the cospicuous fine tuning problem which arises if one gives
instead the couplings of the bare Lagrangian. To show the practical character
of this formulation we deduce the perturbative expansion for the vertex
functions in terms of the physical coupling at the subtraction point
and perform one loop calculations. In particular we analyze to this order some
ST identities and compute the nine bare couplings. We give a schematic proof of
perturbative renormalizability.Comment: 25 pages + 4 figures appended as PostScript file, LaTeX style, UPRF
93-388, explanations adde
BRS symmetry for Yang-Mills theory with exact renormalization group
In the exact renormalization group (RG) flow in the infrared cutoff
one needs boundary conditions. In a previous paper on Yang-Mills theory
we proposed to use the nine physical relevant couplings of the effective action
as boundary conditions at the physical point (these couplings are
defined at some non-vanishing subtraction point ). In this paper we
show perturbatively that it is possible to appropriately fix these couplings in
such a way that the full set of Slavnov-Taylor (ST) identities are satisfied.
Three couplings are given by the vector and ghost wave function normalization
and the three vector coupling at the subtraction point; three of the remaining
six are vanishing (\eg the vector mass) and the others are expressed by
irrelevant vertices evaluated at the subtraction point. We follow the method
used by Becchi to prove ST identities in the RG framework. There the boundary
conditions are given at a non-physical point , so that
one avoids the need of a non-vanishing subtraction point.Comment: 22 pages, LaTeX style, University of Parma preprint UPRF 94-41