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The Dirac equation is generalized to $D+1$ space-time.The conserved angularmomentum operators and their quantum numbers are discussed. The eigenfunctionsof the total angular momenta are calculated for both odd $D$ and even $D$cases. The radial equations for a spherically symmetric system are derived. Theexact solutions for the system with a Coulomb potential are obtainedanalytically. The energy levels and the corresponding fine structure are alsopresented.Comment: 12 pages, no figure, RevTex, Accepted by Inter.J.Mod.Phys.

EXACT SOLUTIONS TO THE DIRAC EQUATION FOR A COULOMB POTENTIAL IN D + 1 DIMENSIONS