A definition of multipartitions of quantum systems into possibly non-factor sub-C* algebras, with a representation theorem showing that some partitions, such as fermionic modes, are not fully representable on tensor-product Hilbert spaces.
Schwinger's Picture of Quantum Mechanics IV: Composition and independence
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abstract
The groupoids description of Schwinger's picture of quantum mechanics is continued by discussing the closely related notions of composition of systems, subsystems, and their independence. Physical subsystems have a neat algebraic description as subgroupoids of the Schwinger's groupoid of the system. The groupoids picture offers two natural notions of composition of systems: Direct and free products of groupoids, that will be analyzed in depth as well as their universal character. Finally, the notion of independence of subsystems will be reviewed, finding that the usual notion of independence, as well as the notion of free independence, find a natural realm in the groupoids formalism. The ideas described in this paper will be illustrated by using the EPRB experiment. It will be observed that, in addition to the notion of the non-separability provided by the entangled state of the system, there is an intrinsic `non-separability' associated to the impossibility of identifying the entangled particles as subsystems of the total system.
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Partitions in quantum theory
A definition of multipartitions of quantum systems into possibly non-factor sub-C* algebras, with a representation theorem showing that some partitions, such as fermionic modes, are not fully representable on tensor-product Hilbert spaces.