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

• Autorzy: Dietmar Dorninger , Helmut Länger , Maciej Maczyński
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

generalized Boolean quasiring; symmetric difference; quantum logic

Kategorie tematyczne

• 06C15: Complemented lattices, orthocomplemented lattices and posets
• 03G12: Quantum logic
• 06E99: None of the above, but in this section
• 81P10: Logical foundations of quantum mechanics; quantum logic

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae - General Algebra and Applications
• Rocznik: 2001
• Tom: 21
• Numer: 2
• Strony: 239-253

Daty

wydano

2001

otrzymano

2001-08-21

Twórcy

autor

Dietmar Dorninger

• Technische Universität Wien, Institut für Algebra und Computermathematik, Wiedner Hauptstraße 8-10, A-1040 Wien

autor

Helmut Länger

• Technische Universität Wien, Institut für Algebra und Computermathematik, Wiedner Hauptstraße 8-10, A-1040 Wien

autor

Maciej Maczyński

• Warsaw University of Technology, Faculty of Mathematics and Information Science, Plac Politechniki 1, PL 00-661 Warsaw, Poland

Bibliografia

• [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.
• [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.
• [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.
• [4] D. Dorninger, H. Länger and M. Maczyński, Lattice properties of ring-like quantum logics, Intern. J. Theor. Phys. 39 (2000), 1015-1026.
• [5] D. Dorninger, H. Länger and M. Maczyński, Concepts of measures on ring-like quantum logics, Rep. Math. Phys. 47 (2001), 167-176.
• [6] G. W. Mackey, The mathematical foundations of quantum mechanics, Benjamin, Reading, MA, 1963.
• [7] M. J. Maczyński, A remark on Mackey's axiom system for quantum mechanics, Bull. Acad. Polon. Sci. 15 (1967), 583- 587.
• [8] V. S. Varadarajan, Geometry of quantum theory. Springer-Verlag, New York 1985.

Identyfikatory

DOI

10.7151/dmgaa.1041