INTEGRATION OF SOURCE-CHARGE CONSTRAINTS IN QUANTUM CHROMODYNAMICS WITH FIXED QUARK AND ANTIQUARK SOURCES

I study the problem of satisfying the source-charge constraints in operator-symmetrized quantum chromodynamics (QCD) with static sources. I show that the color-charge algebras generated by the QCD outer product PA(u,v)=(i2)fABC(uBvC+vCuB) can always be put in the form PA(wa,wb)=iCabcwc, with structure constants Cabc which are totally antisymmetric, but which do not in general satisfy the Jacobi identity. However, total antisymmetry of the C's is enough for the corresponding overlying classical field equations to be derivable from a Lagrangian and to possess a conserved stress-energy tensor, involving a finite number of undetermined constants of integration. I postulate conditions for determining the integration constants when the sources are in a color-singlet state, and use them to fix the overlying classical theory in the qq and the qqq (qqq) cases. © 1979 The American Physical Society.