Quantum-dynamical symmetry groups in curved spaces

The non-vanishing vacuum expectation value of the energy density arising from the spontaneous symmetry breaking in completely unified Yang-Mills-Einstein-Higgs type gauge theories is used to conclude that space-time is strongly curved locally. These localized regions with hadrons are identified. The locality principle in these curved spaces is applied to the quantum mechanical dynamic symmetry groups characterizing internal excitations. Confinement and non-zero triality are examined. Infinite dimensional wave equations are constructed to describe the relativistic hadrons with quantized masses.