Weigel reports about his development of an efficient method, based on scattering data (spectral method) about a scalar field configuration of given topology (static solution to the classical equation of motion), to compute its one-loop effective potential (or vacuum polarization energy, VPE) in a 1 + 1D [[phi].sup.6] (nonrenormalizable
) theory where fluctuations do not naturally decompose into parity eigenstates since the background field may connect inequivalent vacua (not related by a parity transformation).
However, attempts to extend the standard model with gravitons have run into serious theoretical difficulties at high energies (processes with energies close to or above the Planck scale) because of infinities arising due to quantum effects (in other words, gravitation is nonrenormalizable
Thus, the very properties of the singularities lead automatically to improved behavior at the UV scale, even for theories thought to be perturbatively nonrenormalizable
In order to successfully explain neutrino masses in this model without the use of nonrenormalizable
operators , a scalar sextet should be introduced [32, 33].
(Both types are of course nonrenormalizable
in 3+1 dimensions so higher order terms will be generated by quantum mechanics, which we shall return to later).
Like the minimal SM, with its 15 fermions per generation and the standard Higgs doublet [phi](2, 1/2, 1), the minimal SU(5) with Higgs representations [5.sub.H] and [24.sub.H] predicts neutrinos to be massless subject to a tiny O([10.sup.-5]) eV contribution due to nonrenormalizable
Planck scale effect which is nearly 4 orders smaller than the requirement of neutrino oscillation data.
Secondly, any gravitational action including the Einstein-Hilbert one is nonrenormalizable
and should be considered as an effective theory.