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In this paper we start from a basic notion of process, which we structureinto two groupoids, one orthogonal and one symplectic. By introducingadditional structure, we convert these groupoids into orthogonal and symplecticClifford algebras respectively. We show how the orthogonal Clifford algebra,which include the Schr\"oodinger, Pauli and Dirac formalisms, describe theclassical light-cone structure of space-time, as well as providing a basis forthe description of quantum phenomena. By constructing an orthogonal Cliffordbundle with a Dirac connection, we make contact with quantum mechanics throughthe Bohm formalism which emerges quite naturally from the connection, showingthat it is a structural feature of the mathematics. We then generalise theapproach to include the symplectic Clifford algebra, which leads us to anon-commutative geometry with projections onto shadow manifolds. These shadowmanifolds are none other than examples of the phase space constructed by Bohm.We also argue that this provides us with a mathematical structure that fits theimplicate-explicate order proposed by Bohm.

Process, Distinction, Groupoids and Clifford Algebras: an Alternative View of the Quantum Formalism