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Author Lev, Felix
Source arXiv.org
Content type Text
File Format PDF
Date of Submission 2003-08-29
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Natural sciences & mathematics ♦ Physics
Subject Keyword High Energy Physics - Theory ♦ physics:hep-th
Abstract The modern quantum theory is based on the assumption that quantum states are represented by elements of a complex Hilbert space. It is expected that in future quantum theory the number field will be not postulated but derived from more general principles. We consider the choice of the number field in quantum theory based on a Galois field (GFQT) discussed in our previous publications. Since any Galois field is not algebraically closed, in the general case there is no guarantee that even a Hermitian operator necessarily has eigenvalues. We assume that the symmetry algebra is the Galois field analog of the de Sitter algebra so(1,4) and consider spinless irreducible representations of this algebra. It is shown that the Galois field analog of complex numbers is the minimal extension of the residue field modulo $p$ for which the representations are fully decomposable.
Description Reference: Finite Fields and Their Applications, Vol. 12, 336-355 (2006)
Educational Use Research
Learning Resource Type Article
Page Count 27


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