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Book chapter

Feynman geometries

In this paper we introduce a notion of Feynman geometry on which quantum fi eld theories could be properly defi ned. A strong Feynman geometry is a geometry when the vector space of A-infinity structures is nite dimensional. A weak Feynman geometry is a geometry when the vector space of A-infinity structures is in nite dimensional while the relevant operators are of trace-class. We construct families of Feynman geometries with "continuum" as their limit.