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I derive from the quantum-chromodynamic Lagrangian differential laws discribing motions and interactions of an infinite set of string operators—locally gauge-invariant color-singlet operators. By truncating the set, I obtain a q−q¯ wave equation with a confinement potential, and also a jet-fragmentation equation which describes splitting of a q−q¯ string and creation of I=0 vector mesons. I argue for the validity of the perturbative treatment of the string operators

Equation of motion for string operators in quantum chromodynamics