A NOVEL LOOK AT THE MICHAEL LATTICE SUM RULES

TL;DR

This paper revisits the Michael lattice sum rules for quark-antiquark flux tubes, identifies necessary corrections, and discusses how the total field energy differs from the interquark potential, challenging conventional understanding.

Contribution

It provides a corrected derivation of the Michael lattice sum rules and highlights discrepancies between field energy and potential in the Minkowski framework.

Findings

Conventional sum rules require essential corrections.

Total Minkowski field energy does not match the interquark potential.

Implications challenge traditional notions of energy-potential relations.

Abstract

We reconsider the derivation of the Michael lattice sum rules, which relate the energy and action stored in a flux tube of a quark-antiquark pair to the static interquark potential, and show that they require essential corrections. We then find, using the coupling constant sum rule of Karsch, that the total Minkowski field energy does not match the interquark potential, if one follows conventional notions. The implications of this result are discussed.