A fuzzy three sphere and fuzzy tori | Zendy

Brian P. Dolan | Zendy; Denjoe O’Connor | Zendy

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A fuzzy three sphere and fuzzy tori

Author(s) -

Brian P. Dolan,

Denjoe O’Connor

Publication year - 2003

Publication title -

journal of high energy physics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.998

H-Index - 261

eISSN - 1126-6708

pISSN - 1029-8479

DOI - 10.1088/1126-6708/2003/10/060

Subject(s) - mathematics , fuzzy sphere , fuzzy logic , linear subspace , fuzzy subalgebra , fuzzy number , pure mathematics , algebra over a field , torus , eigenvalues and eigenvectors , mathematical analysis , fuzzy set , geometry , computer science , noncommutative geometry , physics , artificial intelligence , quantum mechanics

A fuzzy circle and a fuzzy 3-sphere are constructed as subspaces of fuzzycomplex projective spaces, of complex dimension one and three, by modifying theLaplacians on the latter so as to give unwanted states large eigenvalues. Thisleaves only states corresponding to fuzzy spheres in the low energy spectrum(this allows the commutative algebra of functions on the continuous sphere tobe approximated to any required degree of accuracy). The construction of afuzzy circle opens the way to fuzzy tori of any dimension, thus circumventingthe problem of power law corrections in possible numerical simulations on thesespaces.Comment: 19 pages, typeset in LaTeX, uses youngtab.st

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