Concepts of measures on ring-like quantum logics. (English) Zbl 0980.81009
Summary: The concepts of \(Q\)-valued measures, observables and states are introduced for ring-like quantum logics providing a unified approach to the basic notions of axiomatic quantum mechanics. Consequences of the existence of certain \(Q\)-valued measures for the underlying ring-like structures are investigated and the dependence of \(Q\)-valued measures on certain algebraic properties of ring-like quantum logics is studied. Moreover, links to the lattice-theoretic model of quantum logics are established.
MSC:
| 81P10 | Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects) |
Keywords:
Boolean quasiring; bounded lattice; involutory antiautomorphism; \(Q\)-valued measures; observables; states; axiomatic quantun mechanicsReferences:
| [1] | Dorninger, D.; Länger, H.; Ma̧czyński, M., Demonstratio Math., 30, 215-232 (1997) · Zbl 0879.06005 |
| [2] | Dorninger, D.; Länger, H.; Ma̧czyński, M., Österr. Akad. Wiss. Math.-Natur. Kl. Sitzungsber. II, 206, 279-289 (1997) · Zbl 0945.03095 |
| [3] | Dorninger, D.; Länger, H.; Ma̧czyński, M., Rep. Math. Phys., 43, 499-515 (1999) · Zbl 1056.81004 |
| [4] | D. Dorninger, H. Länger and M. Ma̧czyński: Lattice properties of ring-like quantum logics, Intern, J. Theor. Phys. (to appear).; D. Dorninger, H. Länger and M. Ma̧czyński: Lattice properties of ring-like quantum logics, Intern, J. Theor. Phys. (to appear). |
| [5] | Varadarajan, V. S., Geometry of Quantum Theory (1985), Springer: Springer New York · Zbl 0581.46061 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
