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Classical and Quantum Mechanics in Auxiliary Algebras
Phys. Rev. D 5, 300 – Published 15 January, 1972
DOI: https://doi.org/10.1103/PhysRevD.5.300
Abstract
A canonical algebra is defined as the algebraic structure common to classical and quantum mechanics. It is a linear space equipped with two bilinear operations: an associative product, and a Lie product which is a derivation with respect to the associative product. In addition, the Lie products of the generators of this algebra are constants. The problem of the algorithmic formulation of a canonical algebra in terms of an auxiliary associative algebra is solved. The first part of the problem consists of finding all auxiliary algebras which can algorithmically support a canonical structure. The second part consists of finding all canonical algebras which can be formulated in terms of a given auxiliary structure.
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