Spectral triples and manifolds with boundary

Bruno Iochum (1, 2) , Cyril Levy (1, 2)

1 CPT - Centre de Physique Théorique - UMR 6207
2 CPT - Centre de Physique Théorique - UMR 7332

We investigate manifolds with boundary in noncommutative geometry. Spectral triples associated to a symmetric differential operator and a local boundary condition are constructed. For a classical Dirac operator with a chiral boundary condition, we show that there is no tadpole.

Mots clés: spectral triple; manifold; boundary; tadpole

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]

Bruno Iochum, Cyril Levy. Spectral triples and manifolds with boundary. Journal of Functional Analysis, 2011, 260 (1), pp.117-134. ⟨10.1016/j.jfa.2010.09.006⟩. ⟨hal-00448475v2⟩