In terms of 2×2 vector matrices, we present the realisation of Hurwitz algebras that preserve the correspondence between the geometry of vector spaces used in classical physics and the underlined algebraic basis of quantum theory. A variation to the one originally proposed by M.Zorn is the multiplication rule used. We show that our multiplication is not necessarily nonassociative; the realisation is commutative and associative of the real and complex numbers, the real quaternions preserve associativity, and an alternative algebra is generated by the real octonion matrices. The-the Extending the arbitrary dimensions to the calculus of matrices (matrix elements valued with Hurwitz algebra) is straightforward. The applications of the results obtained to the extensions of the standard Hilbert space formulation of quantum physics and to the mechanical alternative wave formulation of classical field theory are briefly discussed.
Author (s) Details
RCQCE – Research Center for Quantum Communication, Holon Academic Institute of Technology, 52 Golomb St., Holon 58102, Israel.
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