Scalar model of SU(N) glueball à la Heisenberg

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.

Comments: 2 figures, 8 pages