Algebraic and Differential Structures in Renormalized Perturbation Quantum Field Theory

摘要

Some of the algebraic and differential geometric structures underlying the process of reuormalization in perturbation quantum field theory are discussed. It is shown, in particular, that the combinatorics resulting from the perturbative expansion of the transition amplitude and the relation of this expansion to the Hausdorff series leads naturally to consider the Hopf algebra of decorated rooted trees, its relation to the BPHZ Forest formula of renormalization and the geometrical interpretation of the latter in terms of left invariant forms.