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We investigate the nucleon's transverse spin-dependent structure functiong_2(x, Q^{2}) in the framework of the operator product expansion and therenormalization group. We construct the complete set of the twist-3 operatorsfor the flavor singlet channel, and give the relations among them. We developan efficient, covariant approach to derive the anomalous dimension matrix ofthe twist-3 singlet operators by computing the off-shell Green's functions. Asan application, we investigate the renormalization mixing for the lowest momentcase, including the operators proportional to the equations of motion as wellas the ``alien'' operators which are not gauge-invariant.Comment: 13 pages, 13 Postscript figures, psfig.sty and here.sty are require

Renormalization of Gauge-Invariant Operators for the Structure Function g2(x, Q2)