Peirce, Clifford, and quantum theory

Abstract

Beginning in 1870 Charles Sanders Peirce published a series of papers on a "logic of relations," which corresponded to a linear associative algebra. This algebra is related by a linear transformation to quaternions and thus to the C(3, 0) algebra of William Kingdon Clifford. This Clifford algebra contains the Pauli matrices and so constitutes an operator basis for the nonrelativistic quantum theory of spin one-half particles. A further unification is achieved by taking the wave functions themselves to be 2 × 2 matrices which are Peirce logical operators and also elements of the Clifford algebra. Thus we have discovered a direct path from the Peirce logic to quantum theory. A diagrammatic method follows from the Peirce/Clifford algebraic approach and is suitable for describing particle interactions.