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The octonionic eigenvalue problem

By Stefano De Leo and Gisele Ducati

Abstract

By using a real matrix translation, we propose a coupled eigenvalue problem for octonionic operators. In view of possible applications in quantum mechanics, we also discuss the hermiticity of such operators. Previous difficulties in formulating a consistent octonionic Hilbert space are solved by using the new coupled eigenvalue problem and introducing an appropriate scalar product for the probability amplitudes.Comment: 21 page

Topics: Mathematical Physics
Year: 2012
DOI identifier: 10.1088/1751-8113
OAI identifier: oai:arXiv.org:1208.4999

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