This article presents and compares various algebraic structures that arise in axiomatic unsharp quantum physics. We begin by stating some basic principles that such an algebraic structure should encompass. Following G. Mackey and G. Ludwig, we first consider a minimal state-effect-probability (minimal SEFP) structure. In order to include partial operations of sum and difference, an additional axiom is postulated and a SEFP structure is obtained. It is then shown that a SEFP structure is equivalent to an effect algebra with an order determining set of states. We also consider σ-SEFP structures and show that these structures distinguish Hilbert space from incomplete inner product spaces. Various types of sharpness are discussed and under what conditions a Brouwer complementation can be defined to obtain a BZ-poset is investigated. In this case it is shown that every effect has a best lower and upper sharp approximation and that the set of all Brouwer sharp effects form an orthoalgebra

Cattaneo, G., Gudder, S. (1999). Algebraic Structures Arising in Axiomatic Unsharp Quantum Physics. FOUNDATIONS OF PHYSICS, 29(10), 1607-1637 [10.1023/A:1018862721580].

Algebraic Structures Arising in Axiomatic Unsharp Quantum Physics

CATTANEO, GIANPIERO;
1999

Abstract

This article presents and compares various algebraic structures that arise in axiomatic unsharp quantum physics. We begin by stating some basic principles that such an algebraic structure should encompass. Following G. Mackey and G. Ludwig, we first consider a minimal state-effect-probability (minimal SEFP) structure. In order to include partial operations of sum and difference, an additional axiom is postulated and a SEFP structure is obtained. It is then shown that a SEFP structure is equivalent to an effect algebra with an order determining set of states. We also consider σ-SEFP structures and show that these structures distinguish Hilbert space from incomplete inner product spaces. Various types of sharpness are discussed and under what conditions a Brouwer complementation can be defined to obtain a BZ-poset is investigated. In this case it is shown that every effect has a best lower and upper sharp approximation and that the set of all Brouwer sharp effects form an orthoalgebra
Articolo in rivista - Articolo scientifico
algebraic, structures, arising, axiomatic, unsharp, quantum, mechanics
English
1607
1637
31
Cattaneo, G., Gudder, S. (1999). Algebraic Structures Arising in Axiomatic Unsharp Quantum Physics. FOUNDATIONS OF PHYSICS, 29(10), 1607-1637 [10.1023/A:1018862721580].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/20475
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