- 12-85 John R. Klauder
- Divergences in Scalar Quantum Field Theory: The Cause and the Cure
Aug 6, 12
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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
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.