Coherent quantum logic
The author, unsatisfied with the von Neumann quantum logic, pursues the structural parallel between set algebra and linear algebra of Grassmann and Peano. Along these lines he compares three types of quantum logic: (1) the lattic logic of von Neumann, (2) a Clifford algebraic logic, and (3) a Grassmann algebraic logic. The last quantum logic is recommended as the most plausible one because of the following reasons: (1) It is highly symmetric; (2) the unimodular groups of the Peano algebras include the time-space structural group, which is now to be regarded as the unimodular group SL(2,\({\mathbb{C}})\) of two-component spinors, or its higher dimensional analogues SL(N,\({\mathbb{C}})\); (3) the isomorphism of the algebras of classes and sets seems to resolve basic conceptual problems of time-space structure.
scientific article; zbMATH DE number 4002095