Article

Communications in Mathematical Physics

, Volume 307, Issue 1, pp 101-131

Quantum Isometries of the Finite Noncommutative Geometry of the Standard Model

  • Jyotishman BhowmickAffiliated withAbdus Salam International Center for Theoretical Physics (ICTP)
  • , Francesco D’AndreaAffiliated withScuola Internazionale Superiore di Studi Avanzati (SISSA)
  • , Ludwik DąbrowskiAffiliated withScuola Internazionale Superiore di Studi Avanzati (SISSA) Email author 

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Abstract

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 × 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.