On restricting first order form of gauge theories to one-loop order

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. (C) 2021 Elsevier Inc. All rights reserved.