Effective Criticality and Stability of the Double Well
Coincident Pair Configuration

David N. Williams

Randall Laboratory of Physics
The University of Michigan
Ann Arbor, MI 48109-1120
June 7, 1989

Abstract: We show that the coincident instanton--anti-instanton pair configuration in the (1+0)-dimensional, double well model, defined according to a theory presented elsewhere, is an effective critical point of the Euclidean action if it exists and has regularity properties; and is stable if it is also unique. On the way to showing stability we prove a positivity preserving property of the (1+0)-dimensional double well classical field equation with external sources.

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