Explicit construction of constrained instantons

TL;DR

This paper develops a method to explicitly construct constrained instantons in four-dimensional theories, demonstrating their existence as finite action solutions with specific constraints in phi^4 and SU(2) Yang-Mills-Higgs theories.

Contribution

It provides a calculational scheme for constructing constrained instantons and shows their existence as finite action solutions with unique constraints in lowest order.

Findings

Constrained instantons exist as finite action solutions with exponential fall off.

Explicit construction of constrained instantons in phi^4 and SU(2) Yang-Mills-Higgs theories.

Unique constraints are identified for the existence of these solutions.

Abstract

Instantons in massless theories do not carry over to massive theories due to Derrick's theorem. This theorem can, however, be circumvented, if a constraint that restricts the scale of the instanton is imposed on the theory. Constrained instantons are considered in four dimensions in phi^4 theory and SU(2) Yang-Mills-Higgs theory. In each of these theories a calculational sceme is set up and solved in the lowest few orders in the mass parameter in such a way that the need for a constraint is exhibited clearly. Constrained instantons are shown to exist as finite action solutions of the field equations with exponential fall off only for specific constraints that are unique in lowest order in the mass parameter in question.