Letters in Mathematical Physics

, Volume 105, Issue 10, pp 1413–1425 | Cite as

Perturbative Renormalisation for Not-Quite-Connected Bialgebras



We observe that the Connes–Kreimer Hopf-algebraic approach to perturbative renormalisation works not just for Hopf algebras but more generally for filtered bialgebras B with the property that B0 is spanned by group-like elements (e.g. pointed bialgebras with the coradical filtration). Such bialgebras occur naturally both in quantum field theory, where they have some attractive features, and elsewhere in combinatorics, where they cover a comprehensive class of incidence bialgebras. In particular, the setting allows us to interpret Möbius inversion as an instance of renormalisation.

Mathematics Subject Classification

Primary 81T15 Secondary 16T10 16T30 


perturbative renormalisation bialgebras 


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© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Departament de matemàtiquesUniversitat Autònoma de BarcelonaBellaterra (Barcelona)Spain

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