Quantum Isometries of the finite noncommutative geometry of the Standard Model

Details Quantum Isometries of the finite noncommutative geometry of the Standard Model Quantum Isometries of the finite noncommutative geometry of the Standard Model

2010-09-15

arxiv.org/abs/1009.2850v3

Commun.Math.Phys.307:101-131,2011

Mathematics

Quantum Algebra

29 pages, no figures v3: minor changes

Scientific paper

10.1007/s00220-011-1301-2

We compute the quantum isometry group of the finite noncommutative geometry F describing the internal degrees of freedom in the Standard Model of particle physics. We show that this provides genuine quantum symmetries of the spectral triple corresponding to M x F where M is a compact spin manifold. We also prove that the bosonic and fermionic part of the spectral action are preserved by these symmetries.

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