Relativistic action at a distance and fields

TL;DR

This paper explores relativistic action-at-a-distance theories, generalizes a linearly rising potential model, and connects it with a field theory similar to strong interaction models, proposing a simpler action-at-a-distance formulation.

Contribution

It introduces a relativistic non-instantaneous action-at-a-distance formulation for a linearly rising potential and links it to a known strong interaction field model, also proposing a Yang-Mills action-at-a-distance approach.

Findings

Constructed a field theory matching Rivacoba's potential model.

Showed the action-at-a-distance form is simpler than the Lagrangian theory.

Proposed a new action-at-a-distance description for Yang-Mills interactions.

Abstract

After a brief review of the field formulations and the relativistic non-instantaneous action-at-a-distance formulations of some well known classical theories, we study Rivacoba's generalization of a theory with a linearly rising potential as a relativistic non-instantaneous action-at-a-distance theory. For this case we construct the corresponding field theory, which turns out to coincide with a model proposed by Kiskis to describe strong interactions. We construct the action functional for this field theory. Although this model belongs to the class of Lagrangian theories with higher derivatives, it is shown that its action-at-a-distance counterpart has a much simpler form. A proposal to construct an action-at-a-distance description of Yang-Mills interactions is also presented.