The Meson Model on the Basis of the String Solution of the Heisenberg Equation

TL;DR

This paper develops a meson model based on a string-like solution to the Heisenberg equation, proposing a quantum description of non-local objects such as strings and flux tubes.

Contribution

It introduces a novel non-local solution to the Heisenberg equation and applies it to model mesons as rotating strings with quarks at their ends.

Findings

Found a regular, finite-energy non-local solution in the Heisenberg equation.

Proposed a string-based meson model with rotating strings and quarks.

Suggested quantum interpretation of non-local objects like strings and membranes.

Abstract

The axially symmetric non-local solution in the Heisenberg equation is found. It is regular in the whole space and has the finite energy on the unit of length according to this we may consider the solution as a string. Taking the non-local spherically symmetric solution, which was found by Finkelstein et. al., and our solution in account we suggest to consider the Heisenberg equation as a quantum equation for non-local objects (strings, flux tubes, membranes and so on). The received solution is used for the obtaining the meson model as a rotating string with the quark on its ends.