Concrete Quantum Logics and Delta-Logics, States and Delta-States

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F17%3A00315747" target="_blank" >RIV/68407700:21230/17:00315747 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/s10773-017-3359-x" target="_blank" >http://dx.doi.org/10.1007/s10773-017-3359-x</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s10773-017-3359-x" target="_blank" >10.1007/s10773-017-3359-x</a>

Result language
angličtina
Original language name
Concrete Quantum Logics and Delta-Logics, States and Delta-States
Original language description
By a concrete quantum logic (in short, by a logic) we mean the orthomodular poset that is set-representable. If L = (Omega, L) is a logic and L is closed under the formation of symmetric difference, Delta, we call L a Delta-logic. In the first part we situate the known results on logics and states to the context of Delta-logics and Delta-states (the Delta-states are the states that are subadditive with respect to the symmetric difference). Moreover, we observe that the rather prominent logic epsilon(even)(Omega) of all even- coeven subsets of the countable set Omega possesses only Delta-states. Then we show when a state on the logics given by the divisibility relation allows for an extension as a state. In the next paragraph we consider the so called density logic and its Delta-closure. We find that the Delta-closure coincides with the power set. Then we investigate other properties of the density logic and its factor.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10300 - Physical sciences

Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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