, Volume 29, Issue 8, pp 805-814

Tensor product of frame manuals

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Since its first use, there has been widespread dissatisfaction with the Hilbert-space tensor product as a device for coupling the Hilbert-space models of two separated quantum mechanical systems. The Hilbert-space model is paraphrased manual-theoretically by the assertion that quantum mechanical entities are represented by frame manuals. There is a natural, heuristically straightforward tensor product for (unital) manuals, and it is natural therefore to ask whether the tensor product of frame manuals might serve as an alternative model of separated quantum mechanical systems. It is shown that the states on a tensor product of complex frame manuals give rise uniquely to sesquilinear forms on the tensor product of the underlying Hibert spaces. In certain cases, these in turn give rise to operators, which, however, are not generally positive, and which, even if compact, need not be trace-class.