Instanton constraints and renormalization

TL;DR

This paper examines how constraints in quantum field theory instantons must also be renormalized, revealing that only renormalizable constraints are viable for consistent quantum corrections.

Contribution

It demonstrates that constraints in instanton calculations require renormalization, highlighting the necessity for constraints to be renormalizable in quantum field theories.

Findings

Constraints need to be renormalized alongside fields.

Non-renormalizable constraints are generally not permissible.

The study focuses on $$-theory with negative coupling.

Abstract

The renormalization is investigated of one-loop quantum fluctuations around a constrained instanton in $\phi ^4$-theory with negative coupling. It is found that the constraint should be renormalized also. This indicates that in general only renormalizable constraints are permitted.