%0 Journal Article %J Comm. Math. Phys. 279 (2008) 77-116 %D 2008 %T The Isospectral Dirac Operator on the 4-dimensional Orthogonal Quantum Sphere %A Francesco D'Andrea %A Ludwik Dabrowski %A Giovanni Landi %X Equivariance under the action of Uq(so(5)) is used to compute the left regular and (chiral) spinorial representations of the algebra of the quantum Euclidean 4-sphere S^4_q. These representations are the constituents of a spectral triple on this sphere with a Dirac operator which is isospectral to the canonical one of the spin structure of the round undeformed four-sphere and which gives metric dimension four for the noncommutative geometry. Non-triviality of the geometry is proved by pairing the associated Fredholm module with an `instanton\\\' projection. A real structure which satisfies all required properties modulo a suitable ideal of `infinitesimals\\\' is also introduced. %B Comm. Math. Phys. 279 (2008) 77-116 %G en_US %U http://hdl.handle.net/1963/2567 %1 1553 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-01-18T11:00:40Z\\nNo. of bitstreams: 1\\n0611100v1.pdf: 351975 bytes, checksum: 8dd0f817683bd7782e5110ca6b585b91 (MD5) %R 10.1007/s00220-008-0420-x