Communications in Mathematical Physics

, Volume 117, Issue 4, pp 673–683

The action functional in non-commutative geometry

  • A. Connes

DOI: 10.1007/BF01218391

Cite this article as:
Connes, A. Commun.Math. Phys. (1988) 117: 673. doi:10.1007/BF01218391


We establish the equality between the restriction of the Adler-Manin-Wodzicki residue or non-commutative residue to pseudodifferential operators of order −n on ann-dimensional compact manifoldM, with the trace which J. Dixmier constructed on the Macaev ideal. We then use the latter trace to recover the Yang Mills interaction in the context of non-commutative differential geometry.

Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • A. Connes
    • 1
  1. 1.I.H.E.S.Bures-sur-YvetteFrance