, Volume 30, Issue 10, pp 1273-1292

Correspondence principle for the quantum net

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Finkelstein's suggestion for a flexible logic is taken up in the context of his causal net theory. We interpret on the net certain concepts that are first expressed in terms of the canonical “flexible logic” of the macroscopic world, namely, the logic of sheaves over the manifold model, here taken to be flat. From this we infer a correspondence principle in the form of a simple (model-dependent) semantics which translates certain concepts between the purely quantum world of the net and the familiar classical-quantum hybridized world of the macroscopic model. As an application, we derive and solve the reticular version of the massless Dirac equation by analyzing the Dirac operator on the net, where its behavior is easily apprehended.