26 research outputs found
Implicit Regularization and Renormalization of QCD
We apply the Implicit Regularization Technique (IR) in a non-abelian gauge
theory. We show that IR preserves gauge symmetry as encoded in relations
between the renormalizations constants required by the Slavnov-Taylor
identities at the one loop level of QCD. Moreover, we show that the technique
handles divergencies in massive and massless QFT on equal footing.Comment: (11 pages, 2 figures
On the equivalence between Implicit Regularization and Constrained Differential Renormalization
Constrained Differential Renormalization (CDR) and the constrained version of
Implicit Regularization (IR) are two regularization independent techniques that
do not rely on dimensional continuation of the space-time. These two methods
which have rather distinct basis have been successfully applied to several
calculations which show that they can be trusted as practical, symmetry
invariant frameworks (gauge and supersymmetry included) in perturbative
computations even beyond one-loop order.
In this paper, we show the equivalence between these two methods at one-loop
order. We show that the configuration space rules of CDR can be mapped into the
momentum space procedures of Implicit Regularization, the major principle
behind this equivalence being the extension of the properties of regular
distributions to the regularized ones.Comment: 16 page
Comparing Implicit, Differential, Dimensional and BPHZ Renormalisation
We compare a momentum space implicit regularisation (IR) framework with other
renormalisation methods which may be applied to dimension specific theories,
namely Differential Renormalisation (DfR) and the BPHZ formalism. In
particular, we define what is meant by minimal subtraction in IR in connection
with DfR and dimensional renormalisation (DR) .We illustrate with the
calculation of the gluon self energy a procedure by which a constrained version
of IR automatically ensures gauge invariance at one loop level and handles
infrared divergences in a straightforward fashion. Moreover, using the
theory setting sun diagram as an example and comparing explicitly
with the BPHZ framework, we show that IR directly displays the finite part of
the amplitudes. We then construct a parametrization for the ambiguity in
separating the infinite and finite parts whose parameter serves as
renormalisation group scale for the Callan-Symanzik equation. Finally we argue
that constrained IR, constrained DfR and dimensional reduction are equivalent
within one loop order.Comment: 21 pages, 2 figures, late