Geodesic
Ring-like structures with unique symmetric difference related to quantum logic
Discussiones Mathematicae. General Algebra and Applications, Tome 21 (2001) no. 2, pp. 239-253.

Voir la notice de l'article provenant de la source Library of Science

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.
Keywords: generalized Boolean quasiring, symmetric difference, quantum logic 
@article{DMGAA_2001_21_2_a8,
     author = {Dorninger, Dietmar and L\"anger, Helmut and Maczy\'nski, Maciej},
     title = {Ring-like structures with unique symmetric difference related to quantum logic},
     journal = {Discussiones Mathematicae. General Algebra and Applications},
     pages = {239--253},
     publisher = {mathdoc},
     volume = {21},
     number = {2},
     year = {2001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGAA_2001_21_2_a8/}
}
TY  - JOUR
AU  - Dorninger, Dietmar
AU  - Länger, Helmut
AU  - Maczyński, Maciej
TI  - Ring-like structures with unique symmetric difference related to quantum logic
JO  - Discussiones Mathematicae. General Algebra and Applications
PY  - 2001
SP  - 239
EP  - 253
VL  - 21
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGAA_2001_21_2_a8/
LA  - en
ID  - DMGAA_2001_21_2_a8
ER  - 
%0 Journal Article
%A Dorninger, Dietmar
%A Länger, Helmut
%A Maczyński, Maciej
%T Ring-like structures with unique symmetric difference related to quantum logic
%J Discussiones Mathematicae. General Algebra and Applications
%D 2001
%P 239-253
%V 21
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGAA_2001_21_2_a8/
%G en
%F DMGAA_2001_21_2_a8
Dorninger, Dietmar; Länger, Helmut; Maczyński, Maciej. Ring-like structures with unique symmetric difference related to quantum logic. Discussiones Mathematicae. General Algebra and Applications, Tome 21 (2001) no. 2, pp. 239-253. http://geodesic.mathdoc.fr/item/DMGAA_2001_21_2_a8/

[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.