Nonlocality and Gleason's lemma. Part I. Deterministic theories

J. S. Bell's classic 1966 review paper on the foundations of quantum mechanics led directly to the Bell nonlocality theorem. It is not widely appreciated that the review paper contained the basic ingredients needed for a nonlocality result which holds in certain situations where the Bell inequality is not violated. We present in this paper a systematic formulation and evaluation of an argument due to Stairs in 1983, which establishes a nonlocality result based on the Bell-Kochen-Specker paradox in quantum mechanics.     

Multiple local solutions to nonlinear control processes

We use the topological tool of Nielsen fixed-point theory to study the controllability of perturbed linear control processes whose control space can be reduced to a finite-dimensional one. These methods produce a lower bound on the number of controls that achieve a given target. We concentrate particularly on the case where the perturbation has sublinear growth, and we exhibit examples of multiple controls of various types that are detected by the Nielsen theory method.This research was partly supported by the Research Grant Teoria del Controllo dei Sistemi Dinamici, Ministero della Pubblica Istruzione, Roma, Italy.     

A nonperturbative description ofN \bar N annihilation

A nonperturbative picture ofN \(\bar N\) annihilation is proposed. In particular, different parts of the nucleon and the antinucleon do not behave independently, but are tied together by their topological charge. We describe theN \(\bar N\) state as a coherent soliton-antisoliton configuration, and argue that vector mesons play an important role in the decay process. SomeS-wave selection rules are derived. Their relevance to the present LEAR experiments is discussed.