Restricting loop expansions in gauge theories coupled to matter

TL;DR

This paper presents a method to quantize gauge theories with matter fields using Lagrange multipliers, restricting quantum corrections to one-loop order, ensuring renormalizability and unitarity.

Contribution

It introduces a novel approach employing Lagrange multipliers to limit loop corrections in gauge theories coupled to matter, enhancing their quantum consistency.

Findings

Quantization with Lagrange multipliers yields at most one-loop corrections.

The approach ensures renormalizability and unitarity of gauge theories.

Scalar fields can be coupled to gauge fields to restrict loop effects to one-loop order.

Abstract

Quantizing any model in which a Lagrange multiplier (LM) field is used to restrict field configurations to those that satisfy the classical equations of motion, leads to at most one-loop radiative corrections. This approach can be used with both the Yang-Mills (YM) and Einstein-Hilbert (EH) action; the resulting theory is both renormalizable and unitary, has a positive energy spectrum and has no negative norm states contributing to physical processes. Although this approach cannot be consistently used with scalar fields alone, scalar fields can be coupled to gauge fields so that loop effects in the gauge sector are restricted to one-loop order in a way that satisfies the usual criterion for a consistent quantum field theory. The tree-level diagrams are those of the classical theory in which the metric couples to the energy-momentum tensor.