# Quantum integrals and anhomomorphic logics - Quantum Physics

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Abstract: The full anhomomorphic logic of coevents $\ascript ^*$ is introduced. Atomsof $\ascript ^*$ and embeddings of the event set $\ascript$ into $\ascript ^*$are discussed. The quantum integral over an event $A$ with respect to a coevent$\phi$ is defined and its properties are treated. Integrals with respect tovarious coevents are computed. Reality filters such as preclusivity andregularity of coevents are considered. A quantum measure $\mu$ that can berepresented as a quantum integral with respect to a coevent $\phi$ is said to1-generate $\phi$. This gives a stronger reality filter that may produce aunique coevent called the ``actual reality- for a physical system. What webelieve to be a more general filter is defined in terms of a double quantumintegral and is called 2-generation. It is shown that ordinary measures do not1 or 2-generate coevents except in a few simple cases. Examples are given whichshow that there are quantum measures that 2-generate but do not 1-generatecoevents. Examples also show that there are coevents that are 2-generated butnot 1-generated. For simplicity only finite systems are considered.

Author: ** Stan Gudder**

Source: https://arxiv.org/