New graph polynomials in parametric QED Feynman integrals

摘要

AbstractIn recent years enormous progress has been made in perturbative quantum field theory by applying methods of algebraic geometry to parametric Feynman integrals for scalar theories. The transition to gauge theories is complicated not only by the fact that their parametric integrand is much larger and more involved. It is, moreover, only implicitly given as the result of certain differential operators applied to the scalar integrandexp(?ΦΓ∕ΨΓ), whereΨΓandΦΓare the Kirchhoff and Symanzik polynomials of the Feynman graphΓ. In the case of quantum electrodynamics we find that the full parametric integrand inherits a rich combinatorial structure fromΨΓandΦΓ. In the end, it can be expressed explicitly as a sum over products of new types of graph polynomials which have a combinatoric interpretation via simple cycle subgraphs ofΓ.]]>