John R. Klauder
Divergences in Scalar Quantum Field Theory: The Cause and the Cure
(26K, LaTex)

ABSTRACT.  Covariant scalar fields exhibit divergences when quantized in two or 
more spacetime dimensions: n\ge2. 
Does perturbation theory, effective theories, the renormalization group, etc., tell 
us all there is to know about these problems? An 
alternative approach identifies the cause of divergences as due to 
the effort to multiplicatively relate two measures that are mutually 
 singular, 
while the cure for those divergences is to introduce an 
O(\hbar) counterterm that converts mutually singular measures into equivalent measures. 
This procedure leads to a nontrivial, divergence-free formulation for 
all n\ge2. Finally, a critical comparison of the new methods 
with traditional procedures is given.