Nonperturbative Quantization of the Cylindrically Symmetric Strongly Oscillating Field

TL;DR

This paper applies a nonperturbative quantization method to classical SU(2) Yang-Mills solutions, removing their problematic long-distance behavior while preserving their short-distance features, advancing understanding of strongly interacting fields.

Contribution

It introduces a nonperturbative quantization approach to classical singular solutions, improving their physical relevance in Yang-Mills theory.

Findings

Elimination of bad long-distance behavior in solutions

Retention of short-distance features

Potential implications for nonperturbative field theory

Abstract

A recent investigation of SU(2) Yang-Mills theory found several classical solutions with bad behaviour at infinity : one of the potential components oscillated and another tended to infinity. In this paper we apply an idea due to Heisenberg about the quantization of strongly interacting nonlinear fields to these classical singular solutions. We find that this quantization procedure eliminates the bad long distance features while retaining the interesting short distance aspects of these solutions.