DOI: 10.1140/epjc/s2002-01022-5
Unrenormalizable theories can be predictive
J. Kubo1, 2 and M. Nunami21 Max-Planck-Institut für Physik, Werner-Heisenberg-Institut, 80805 Munich, Germany
2 Institute for Theoretical Physics, Kanazawa University, Kanazawa 920-1192, Japan
(Received: 28 March 2002 / Revised version: 28 May 2002 / Published online: 31 October 2002)
Abstract
Unrenormalizable theories contain
infinitely many free parameters.
Considering these theories
in terms of the Wilsonian renormalization group (RG),
we suggest a method for
removing this large ambiguity.
Our basic assumption is the existence
of a maximal ultraviolet cutoff
in a cutoff theory, and
we require that
the theory be so fine tuned as to
reach the maximal cutoff.
The theory so obtained behaves as a local
continuum theory to the shortest distance.
In concrete examples of the scalar theory we find that
at least in a certain approximation to
the Wilsonian RG, this requirement enables us
to make unique
predictions in the infrared regime
in terms of a finite number of independent parameters.
Therefore, this method
might provide a way for calculating quantum corrections
in a low-energy effective theory of quantum gravity.
© Società Italiana di Fisica, Springer-Verlag 2003
