On Restricting First Order Form of Gauge Theories to One-Loop Order

TL;DR

This paper demonstrates that by restricting gauge theories to one-loop order using Lagrange multiplier fields, one can compute Green's functions exactly while maintaining renormalizability and unitarity.

Contribution

It introduces a method to eliminate radiative effects beyond one-loop order in gauge theories using Lagrange multiplier fields, ensuring exact Green's function calculations.

Findings

Quantized theories remain renormalizable and unitary with the restriction.

Green's functions can be computed exactly at one-loop order.

Radiative effects beyond one-loop are effectively eliminated.

Abstract

The first order form of the Yang-Mills and Einstein-Hilbert actions are quantized, and it is shown how Green's functions computed using the first and the second order form of these theories are related. Next we show how by use of Lagrange multiplier fields (LM), radiative effects beyond one-loop order can be eliminated. This allows one to compute Green's functions exactly without loss of unitarity. The consequences of this restriction on radiative effects are examined for the Yang-Mills and Einstein-Hilbert actions. In these two gauge theories, we find that the quantized theory is both renormalizable and unitary once the LM field is used to eliminate effects beyond one-loop order.