  We resolve the space-time canonical variables of the relativistic point
particle into inner products of Weyl spinors with components in a Clifford
algebra and find that these spinors themselves form a canonical system with
generalized Poisson brackets. For N particles, the inner products of their
Clifford coordinates and momenta form two NxN Hermitian matrices X and P which
transform under a U(N) symmetry in the generating algebra. This is used as a
starting point for defining matrix mechanics for a point particle in Clifford
space. Next we consider the string. The Lorentz metric induces a metric and a
scalar on the world sheet which we represent by a Jackiw-Teitelboim term in the
action. The string is described by a polymomenta canonical system and we find
the wave solutions to the classical equations of motion for a flat world sheet.
Finally, we show that the SL(2.C) charge and space-time momentum of the
quantized string satisfy the Poincare algebra.
