Communications in Mathematical Physics

, 307:101

Quantum Isometries of the Finite Noncommutative Geometry of the Standard Model

  • Jyotishman Bhowmick
  • Francesco D’Andrea
  • Ludwik Dąbrowski
Article

DOI: 10.1007/s00220-011-1301-2

Cite this article as:
Bhowmick, J., D’Andrea, F. & Dąbrowski, L. Commun. Math. Phys. (2011) 307: 101. doi:10.1007/s00220-011-1301-2

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.

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Jyotishman Bhowmick
    • 1
  • Francesco D’Andrea
    • 2
  • Ludwik Dąbrowski
    • 2
  1. 1.Abdus Salam International Center for Theoretical Physics (ICTP)TriesteItaly
  2. 2.Scuola Internazionale Superiore di Studi Avanzati (SISSA)TriesteItaly