We solve the Gauss law and the corresponding Mandelstam constraints in the loop Hilbert space HL using the prepotential formulation of (d+1) dimensional SU(2) lattice gauge theory. The resulting orthonormal and complete loop basis, explicitly constructed in terms of the d(2d − 1) prepotential intertwining operators, is used to transcribe the gauge dynamics directly in HL without any redundant g...