Scalar model of SU(N) glueball \`a la Heisenberg

TL;DR

This paper develops a nonperturbative scalar field model for SU(N) glueballs using Heisenberg's quantization, deriving an effective Lagrangian and demonstrating the existence of a spherically symmetric glueball solution.

Contribution

It introduces a novel scalar field approach to model SU(N) glueballs nonperturbatively, explicitly calculating Lagrangian coefficients based on group dimensions.

Findings

Derived an effective Lagrangian for scalar fields representing quantum fluctuations.

Calculated Lagrangian coefficients depending on SU(n) and SU(N) dimensions.

Found a spherically symmetric solution that describes a glueball.

Abstract

Nonperturbative model of glueball is studied. The model is based on the nonperturbative quantization technique suggested by Heisenberg. 2- and 4-point Green functions for a gauge potential are expressed in terms of two scalar fields. The first scalar field describes quantum fluctuations of the subgroup $SU(n) \subset SU(N)$, and the second one describes quantum fluctuations of the coset $SU(N) / SU(n)$. An effective Lagrangian for the scalar fields is obtained. The coefficients for all terms in the Lagrangian are calculated, and it is shown that they depend on $\dim SU(n), \dim SU(N)$. It is demonstrated that a spherically symmetric solution describing the glueball does exist.