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Representable Effect Algebras and Observables

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Abstract

We introduce a class of monotone σ-complete effect algebras, called representable, which are σ-homomorphic images of a class of monotone σ-complete effect algebras of functions taking values in the interval [0, 1] and with effect algebra operations defined by points. We exhibit different types of compatibilities and show their connection to representability. Finally, we study observables and show situations when information of an observable on all intervals of the form (−∞, t) gives full information about the observable.

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Acknowledgement

The author is very indebted to anonymous referees for their careful reading and suggestions which helped to improve the readability of the paper.

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Authors and Affiliations

  1. Mathematical Institute, Slovak Academy of Sciences, Štefánikova 49, 814 73, Bratislava, Slovakia

    Anatolij Dvurečenskij

  2. Department of Algebra and Geometry, Palacký University, 771 46, Olomouc, Czech Republic

    Anatolij Dvurečenskij

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  1. Anatolij Dvurečenskij
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Correspondence to Anatolij Dvurečenskij.

Additional information

The paper has been supported by the Slovak Research and Development Agency under the contract APVV-0178-11, the grant VEGA No. 2/0059/12 SAV and by CZ.1.07/2.3.00/20.0051.

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Dvurečenskij, A. Representable Effect Algebras and Observables. Int J Theor Phys 53, 2855–2866 (2014). https://doi.org/10.1007/s10773-014-2083-z

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  • DOI: https://doi.org/10.1007/s10773-014-2083-z

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