Gluonic mass spectrum in the Abelian bag model

Abstract

We consider noninteracting gluons confined in a bag whose volume is proportional to its energy. The asymptotic mass spectrum $\ensuremath{\rho}(m)$ for such a system is derived analytically taking the finite size of the bag into account. The exponent in the mass spectrum is shown to be $\frac{m}{{T}_{0}}\ensuremath{-}\ensuremath{\eta}{(\frac{m}{{T}_{0}})}^{\frac{1}{3}}$, where ${T}_{0}$ is the limiting temperature and $\ensuremath{\eta}$ is a shape-dependent positive number. Numerical comparison with exact calculations is made for one specific shape. It is pointed out that the curvature correction term in the exponent has important thermodynamic implications.