Ring-like structures with unique symmetric difference related to quantum logic

Dietmar Dorninger; Helmut Länger; Maciej Maczyński

Discussiones Mathematicae - General Algebra and Applications (2001)

  • Volume: 21, Issue: 2, page 239-253
  • ISSN: 1509-9415

Abstract

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Ring-like quantum structures generalizing Boolean rings and having the property that the terms corresponding to the two normal forms of the symmetric difference in Boolean algebras coincide are investigated. Subclasses of these structures are algebraically characterized and related to quantum logic. In particular, a physical interpretation of the proposed model following Mackey's approach to axiomatic quantum mechanics is given.

How to cite

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Dietmar Dorninger, Helmut Länger, and Maciej Maczyński. "Ring-like structures with unique symmetric difference related to quantum logic." Discussiones Mathematicae - General Algebra and Applications 21.2 (2001): 239-253. <http://eudml.org/doc/287601>.

@article{DietmarDorninger2001,
abstract = {Ring-like quantum structures generalizing Boolean rings and having the property that the terms corresponding to the two normal forms of the symmetric difference in Boolean algebras coincide are investigated. Subclasses of these structures are algebraically characterized and related to quantum logic. In particular, a physical interpretation of the proposed model following Mackey's approach to axiomatic quantum mechanics is given.},
author = {Dietmar Dorninger, Helmut Länger, Maciej Maczyński},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {generalized Boolean quasiring; symmetric difference; quantum logic; normal forms of symmetric difference; weak associativity; Boolean quasirings; Mackey's approach to axiomatic quantum mechanics},
language = {eng},
number = {2},
pages = {239-253},
title = {Ring-like structures with unique symmetric difference related to quantum logic},
url = {http://eudml.org/doc/287601},
volume = {21},
year = {2001},
}

TY - JOUR
AU - Dietmar Dorninger
AU - Helmut Länger
AU - Maciej Maczyński
TI - Ring-like structures with unique symmetric difference related to quantum logic
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2001
VL - 21
IS - 2
SP - 239
EP - 253
AB - Ring-like quantum structures generalizing Boolean rings and having the property that the terms corresponding to the two normal forms of the symmetric difference in Boolean algebras coincide are investigated. Subclasses of these structures are algebraically characterized and related to quantum logic. In particular, a physical interpretation of the proposed model following Mackey's approach to axiomatic quantum mechanics is given.
LA - eng
KW - generalized Boolean quasiring; symmetric difference; quantum logic; normal forms of symmetric difference; weak associativity; Boolean quasirings; Mackey's approach to axiomatic quantum mechanics
UR - http://eudml.org/doc/287601
ER -

References

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  1. [1] D. Dorninger, H. Länger and M. Maczyński, The logic induced by a system of homomorphisms and its various algebraic characterizations, Demonstratio Math. 30 (1997), 215-232. Zbl0879.06005
  2. [2] D. Dorninger, H. Länger and M. Maczyński, On ring-like structures occurring in axiomatic quantum mechanics, Österreich. Akad. Wiss. Math.-Natur. Kl. Sitzungsber. II 206 (1997), 279-289. Zbl0945.03095
  3. [3] D. Dorninger, H. Länger and M. Maczyński, On ring-like structures induced by Mackey's probability function, Rep. Math. Phys. 43 (1999), 499-515. Zbl1056.81004
  4. [4] D. Dorninger, H. Länger and M. Maczyński, Lattice properties of ring-like quantum logics, Intern. J. Theor. Phys. 39 (2000), 1015-1026. Zbl0967.03055
  5. [5] D. Dorninger, H. Länger and M. Maczyński, Concepts of measures on ring-like quantum logics, Rep. Math. Phys. 47 (2001), 167-176. Zbl0980.81009
  6. [6] G. W. Mackey, The mathematical foundations of quantum mechanics, Benjamin, Reading, MA, 1963. Zbl0114.44002
  7. [7] M. J. Maczyński, A remark on Mackey's axiom system for quantum mechanics, Bull. Acad. Polon. Sci. 15 (1967), 583- 587. Zbl0203.00801
  8. [8] V. S. Varadarajan, Geometry of quantum theory. Springer-Verlag, New York 1985. Zbl0581.46061

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