The slogan “Follow the money” means that finding the source of an organization’s or person’s money may reveal their true nature. In a similar sense, we use the slogan “Follow the math!” to mean that finding “where the mathematics of QM comes from” reveals a good deal about the key concepts and machinery of the theory.
Quantum Logic of Direct-sum Decompositions
June 20, 2017 by
The usual quantum logic, beginning with Birkhoff and Von Neumann, was the logic of closed subspaces of a Hilbert space. This paper develops the more general logic of direct-sum decompositions of a vector space. This allows the treatment of measurement of any self-adjoint operators rather than just the projection operators associated with subspaces.
Counting Direct-sum Decompositions
March 28, 2016 by
This paper uses elementary methods to derive the formulas for and to tablulate (in the case q = 2) two related q-analogs of the Stirling numbers of the second kind and the Bell numbers for direct-sum decompositions (vector space analogs of set partitions) of a finite vector space over a finite field with q elements.