On the basis of Mackey's axiomatic approach to quantum physics or, equivalently, of a ldquostate-event-probabilityrdquo (SEVP) structure, using a quite standard ldquofuzzificationrdquo procedure, a set of unsharp events (or ldquoeffectsrdquo) is constructed and the corresponding ldquostate-effect-probabilityrdquo (SEFP) structure is introduced. The introduction of some suitable axioms gives rise to a partially ordered structure of quantum Brouwer-Zadeh (BZ) poset; i.e., a poset endowed with two nonusual orthocomplementation mappings, a fuzzy-like orthocomplementation, and an intuitionistic-like orthocomplementation, whose set of sharp elements is an orthomodular complete lattice. As customary, by these orthocomplementations the two modal-like necessity and possibility operators are introduced, and it is shown that Ludwig's and Jauch-Piron's approaches to quantum physics are ldquointerpretedrdquo in complete SEFP. As a marginal result, a standard procedure to construct a lot of unsharp realizations starting from any sharp realization of a fixed observable is given, and the relationship among sharp and corresponding unsharp realizations is studied

Cattaneo, G., Laudisa, F. (1994). Axiomatic unsharp quantum theory (From Mackey to Ludwig and Piron). FOUNDATIONS OF PHYSICS, 24(5), 631-683 [10.1007/BF02054668].

Axiomatic unsharp quantum theory (From Mackey to Ludwig and Piron)

CATTANEO, GIANPIERO;LAUDISA, FEDERICO
1994

Abstract

On the basis of Mackey's axiomatic approach to quantum physics or, equivalently, of a ldquostate-event-probabilityrdquo (SEVP) structure, using a quite standard ldquofuzzificationrdquo procedure, a set of unsharp events (or ldquoeffectsrdquo) is constructed and the corresponding ldquostate-effect-probabilityrdquo (SEFP) structure is introduced. The introduction of some suitable axioms gives rise to a partially ordered structure of quantum Brouwer-Zadeh (BZ) poset; i.e., a poset endowed with two nonusual orthocomplementation mappings, a fuzzy-like orthocomplementation, and an intuitionistic-like orthocomplementation, whose set of sharp elements is an orthomodular complete lattice. As customary, by these orthocomplementations the two modal-like necessity and possibility operators are introduced, and it is shown that Ludwig's and Jauch-Piron's approaches to quantum physics are ldquointerpretedrdquo in complete SEFP. As a marginal result, a standard procedure to construct a lot of unsharp realizations starting from any sharp realization of a fixed observable is given, and the relationship among sharp and corresponding unsharp realizations is studied
Articolo in rivista - Articolo scientifico
Quantum mechanics, quantum logic, unsharp quantum theory
English
631
683
53
Cattaneo, G., Laudisa, F. (1994). Axiomatic unsharp quantum theory (From Mackey to Ludwig and Piron). FOUNDATIONS OF PHYSICS, 24(5), 631-683 [10.1007/BF02054668].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/30877
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