The general vector potential (gauge theory) approach for including geometric phase effects in accurate three-dimensional quantum scattering calculations in symmetrized hyperspherical coordinates is applied to the H + D-2(v,j) --> HD(v＇,j＇) + D reaction at 126 values of total energy in the range 0.4-2.4 eV. State-to-state reaction probabilities, integral, and differential cross sections are computed using both the Boothroyd-Keogh-Martin-Peterson (BKMP2) and the Liu-Siegbahn-Truhlar-Horowitz potential energy surfaces for the first six values of total angular momentum (J less than or equal to 5). Calculations are performed on each surface both with and without the geometric phase. Due to symmetry, the effects of the geometric phase are shown to cancel out when contributions from even and odd values of J are added together for both the integral and differential cross sections, at all energies, and independent of which surface is used. These results are consistent with recent experimental results which are in good agreement with theoretical treatments which do not include the geometric phase. Relatively broad transition state resonances are observed in the rotationally resolved integral and differential cross sections. (C) 2000 American Institute of Physics. [S0021-9606(00)01013-8].