Field Redefinition Invariance in Quantum Field Theory
Karyn M. Apfeldorf, Horacio E. Camblong, Carlos R. Ordonez
TL;DR
This paper reexamines the invariance of path integrals under field redefinitions in quantum field theory, highlighting operator-ordering issues and resolving a paradox involving dimensional reduction.
Contribution
It clarifies the role of operator-ordering in field redefinition invariance and addresses a paradox related to dimensional reduction in quantum field theory.
Findings
Field redefinition invariance is subtle and involves operator-ordering considerations.
A paradox in dimensional reduction of quantum fields is resolved.
Operator-ordering issues are crucial for consistent quantum field theory formulations.
Abstract
The issue of field redefinition invariance of path integrals in quantum field theory is reexamined. A ``paradox'' is presented involving the reduction to an effective quantum-mechanical theory of a -dimensional free scalar field in a Minkowskian spacetime with compactified spatial coordinates. The implementation of field redefinitions both before and after the reduction suggests that operator-ordering issues in quantum field theory should not be ignored.
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