  In 1978, Friedberg and Lee introduced the phenomenological soliton bag model
of hadrons, generalizing the MIT bag model developed in 1974 shortly after the
formulation of QCD. In this model, quarks and gluons are confined due to
coupling with a real scalar field $\rho$ which tends to zero outside some
compact region $S\subset{\mathbb R}^3$ determined dynamically from the
equations of motion. The gauge coupling in the soliton bag model is running as
the inverse power of $\rho$ already at the semiclassical level. We show that
this model arises naturally as a consequence of introducing the warped product
metric ${\mathrm{d}}s^2_M + \rho^2{\mathrm{d}}s^2_G$ on the principal
$G$-bundle $P(M,G)\cong M\times G$ with a non-Abelian group $G$ over Minkowski
space $M={\mathbb R}^{3,1}$. Confinement of quarks and gluons in a compact
domain $S\subset{\mathbb R}^3$ is a consequence of the collapse of the bundle
manifold $M\times G$ to $M$ outside $S$ due to shrinking of the group manifold
$G$ to a point. We describe the formation of such regions $S$ as a dynamical
process controlled by the order parameter field $\rho$.
