Notes on Feynman Integrals and Renormalization

I review various aspects of Feynman integrals, regularization and renormalization. Following Bloch, I focus on a linear algebraic approach to the Feynman rules, and I try to bring together several renormalization methods found in the literature from a unifying point of view, using resolutions of singularities. In the second part of the paper, I briefly sketch the work of Belkale, Brosnan resp. Bloch, Esnault and Kreimer on the motivic nature of Feynman integrals.Comment: 39

Hopf algebras in renormalization theory: Locality and Dyson-Schwinger equations from Hochschild cohomology

In this review we discuss the relevance of the Hochschild cohomology of renormalization Hopf algebras for local quantum field theories and their equations of motion.Comment: 29 pages, eps figures; minor changes; final versio

The Hopf algebra of rooted trees in Epstein-Glaser renormalization

We show how the Hopf algebra of rooted trees encodes the combinatorics of Epstein-Glaser renormalization and coordinate space renormalization in general. In particular we prove that the Epstein-Glaser time-ordered products can be obtained from the Hopf algebra by suitable Feynman rules, mapping trees to operator-valued distributions. Twisting the antipode with a renormalization map formally solves the Epstein-Glaser recursion and provides local counterterms due to the Hochschild 1-closedness of the grafting operator $B_+$.Comment: 19p, minor corrections and improvements. To appear in AH

Contesting Europe, contesting identity? An empirical study of party positioning on national and European identity, 1979-2009

As the EU’s political powers expand, so do concerns about its impact on the traditions and identities of the member states. The prediction is that parties will try to capitalize on such concerns and compete over this cultural dimension of European integration. Collective identities will become decisive if and when political parties cue voters to perceive national identities as incompatible with European integration. Yet most extant research focuses on the effects of parties’ general stance toward European integration, while the specific content of partisan massages remains unexplored; in consequence, we know little about if and how parties deliberately mobilise collective identities for or against European integration. By disaggregating party positions on Europe, this paper seeks to explore more closely to what extent parties appeal to national and European identities. Drawing on party manifesto data from the Euromanifestos Project (EMP), I examine the salience and determinants of national and European identity mobilization by national political parties in the EU 15 over the period 1979-2009. The empirical analysis finds only little evidence for an increase in the salience of national and European identity mobilization with on-going EU integration. Patterns of identity mobilization are shown to vary as a function of parties’ ideological positions and political opportunities

A Review of the Political Status of the Trust Territory of the Pacific

Micronesia\u27s strategic location has made it a valuable prize in the quest far overseas bases. Today it is governed by the United States as a strategic trusteeship under the auspices of the United Nations, and the inhabitants of the islands have requested an association with the United Slates, the details of which remain to be negotiated

What is the trouble with Dyson--Schwinger equations?

We discuss similarities and differences between Green Functions in Quantum Field Theory and polylogarithms. Both can be obtained as solutions of fixpoint equations which originate from an underlying Hopf algebra structure. Typically, the equation is linear for the polylog, and non-linear for Green Functions. We argue though that the crucial difference lies not in the non-linearity of the latter, but in the appearance of non-trivial representation theory related to transcendental extensions of the number field which governs the linear solution. An example is studied to illuminate this point.Comment: 5 pages contributed to the proceedings "Loops and Legs 2004", April 2004, Zinnowitz, German