4 research outputs found
Slavnov-Taylor Parameterization for the Quantum Restoration of BRST Symmetries in Anomaly-Free Gauge Theories
It is shown that the problem of the recursive restoration of the
Slavnov-Taylor (ST) identities at the quantum level for anomaly-free gauge
theories is equivalent to the problem of parameterizing the local approximation
to the quantum effective action in terms of ST functionals, associated with the
cohomology classes of the classical linearized ST operator. The ST functionals
of dimension <=4 correspond to the invariant counterterms, those of dimension
>4 generate the non-symmetric counterterms upon projection on the action-like
sector. At orders higher than one in the loop expansion there are additional
contributions to the non-invariant counterterms, arising from known lower order
terms. They can also be parameterized by using the ST functionals. We apply the
method to Yang-Mills theory in the Landau gauge with an explicit mass term
introduced in a BRST-invariant way via a BRST doublet. Despite being
non-unitary, this model provides a good example where the method devised in the
paper can be applied to derive the most general solution for the action-like
part of the quantum effective action, compatible with the fulfillment of the ST
identities and the other relevant symmetries of the model, to all orders in the
loop expansion. The full dependence of the solution on the normalization
conditions is given.Comment: 23 pages. Final version published in the journa
Constructive algebraic renormalization of the abelian Higgs-Kibble model
We propose an algorithm, based on Algebraic Renormalization, that allows the
restoration of Slavnov-Taylor invariance at every order of perturbation
expansion for an anomaly-free BRS invariant gauge theory. The counterterms are
explicitly constructed in terms of a set of one-particle-irreducible Feynman
amplitudes evaluated at zero momentum (and derivatives of them). The approach
is here discussed in the case of the abelian Higgs-Kibble model, where the zero
momentum limit can be safely performed. The normalization conditions are
imposed by means of the Slavnov-Taylor invariants and are chosen in order to
simplify the calculation of the counterterms. In particular within this model
all counterterms involving BRS external sources (anti-fields) can be put to
zero with the exception of the fermion sector.Comment: Jul, 1998, 31 page
On the trace identity in a model with broken symmetry
Considering the simple chiral fermion meson model when the chiral symmetry is
explicitly broken, we show the validity of a trace identity -- to all orders of
perturbation theory -- playing the role of a Callan-Symanzik equation and which
allows us to identify directly the breaking of dilatations with the trace of
the energy-momentum tensor. More precisely, by coupling the quantum field
theory considered to a classical curved space background, represented by the
non-propagating external vielbein field, we can express the conservation of the
energy-momentum tensor through the Ward identity which characterizes the
invariance of the theory under the diffeomorphisms. Our ``Callan-Symanzik
equation'' then is the anomalous Ward identity for the trace of the
energy-momentum tensor, the so-called ``trace identity''.Comment: 11 pages, Revtex file, final version to appear in Phys.Rev.