Results 1 
2 of
2
ALGEBROGEOMETRIC FEYNMAN RULES
"... Abstract. We give a general procedure to construct algebrogeometric Feynman rules, that is, characters of the Connesâ€“Kreimer Hopf algebra of Feynman graphs that factor through a Grothendieck ring of immersed conical varieties, via the class of the complement of the affine graph hypersurface. In par ..."
Abstract

Cited by 19 (9 self)
 Add to MetaCart
(Show Context)
Abstract. We give a general procedure to construct algebrogeometric Feynman rules, that is, characters of the Connesâ€“Kreimer Hopf algebra of Feynman graphs that factor through a Grothendieck ring of immersed conical varieties, via the class of the complement of the affine graph hypersurface. In particular, this maps to the usual Grothendieck ring of varieties, defining motivic Feynman rules. We also construct an algebrogeometric Feynman rule with values in a polynomial ring, which does not factor through the usual Grothendieck ring, and which is defined in terms of characteristic classes of singular varieties. This invariant recovers, as a special value, the Euler characteristic of the projective graph hypersurface complement. The main result underlying the construction of this invariant is a formula for the characteristic classes of the join of two projective varieties. We discuss the BPHZ renormalization procedure in this algebrogeometric context and some motivic zeta functions arising from the partition functions associated to motivic Feynman rules. 1.