Nonlocal Yang-Mills

TL;DR

This paper introduces a simple method to create nonlocal versions of perturbative theories, resulting in finite Green's functions and preserved unitarity, with specific calculations for pure Yang-Mills theory.

Contribution

It provides an explicit procedure for nonlocalizing perturbative theories and demonstrates how to maintain unitarity and finiteness, including the computation of measure factors for Yang-Mills.

Findings

Green's functions are finite to all orders in the nonlocal theory.

Perturbative unitarity is preserved for scalars with nonderivative interactions.

On-shell tree amplitudes remain unaffected by the nonlocal regularization.

Abstract

We present a very simple and explicit procedure for nonlocalizing the action of any theory which can be formulated perturbatively. When the resulting nonlocal field theory is quantized using the functional formalism --- with unit measure factor --- its Green's functions are finite to all orders. The construction also ensures perturbative unitarity to all orders for scalars with nonderivative interactions, however, decoupling is lost at one loop when vector and tensor quanta are present. Decoupling can be restored (again, to all orders) if a suitable measure factor exists. We compute the required measure factor for pure Yang-Mills at order $g^2$ and then use it to evaluate the vacuum polarization at one loop. A peculiar feature of our regularization scheme is that the on-shell tree amplitudes are completely unaffected. This implies that the nonlocal field theory can be viewed as a highly noncanonical quantization of the original, local field equations.