It is argued that geometric algebra, in the form of the multiparticle spacetime algebra, is well-suited to the study of multiparticle quantum theory, with advantages over conventional techniques both in ease of calculation and in providing an intuitive geometric understanding of the results. This is illustrated by comparing the geometric algebra approach for a system of two spin-1/2 particles with the non-relativistic approach of Holland.
S.S. Somaroo, A.N. Lasenby and C.J.L. Doran, Geometric algebra and the causal approach to multiparticle quantum mechanics, J. Math. Phys. 40(7), 3327-3340 (1999)