相关论文: On Motives Associated to Graph Polynomials

We review Deitmar's theory of monoidal schemes to start with, and have a detailed look at the standard examples. It is explained how one can combinatorially study such schemes through a generalization of graph theory. In a more general…

Certain power-counting non-renormalizable theories, including the most general self-interacting scalar fields in four and three dimensions and fermions in two dimensions, have a simplified renormalization structure. For example, in…

We put forward the first analysis of renormalization group flows in an area-metric theory, motivated by spin-foam quantum gravity. Area-metric gravity contains the well-known length-metric degrees of freedom of standard gravity as well as…

We define a birational analog of the motivic zeta function of a reduced polynomial in terms of minimal models. It admits an intrinsic meaning in terms of contact loci of arcs, an analog of a result of Denef and Loeser in the motivic case.…

We exhibit a quantum algorithm for determining the zeta function of a genus g curve over a finite field F_q, which is polynomial in g and log(q). This amounts to giving an algorithm to produce provably random elements of the class group of…

A careful analysis of differential renormalization shows that a distinguished choice of renormalization constants allows for a mathematically more fundamental interpretation of the scheme. With this set of a priori fixed integration…

This work is devoted to the study of the relationships between graph theory and the qualitative analysis of ordinary differential equations, with a special focus on two-dimensional systems. In particular, we reinterpret classical results…

We define motivic analogues of Igusa's local zeta functions. These functions take their values in a Grothendieck group of Chow motives. They specialize to p-adic Igusa local zeta functions and to the topological zeta functions we introduced…

It is shown that for 2D field theories only the first order coefficient of the gravitationally dressed RG $\beta$-function is scheme independent. This is valid even for matter theories with one dimensionless coupling, where the first two…

We provide several properties of the geometric polynomials discussed in earlier works of the authors. Further, the geometric polynomials are used to obtain a closed form evaluation of certain series involving Riemann's zeta function.

We shortly illustrate how the field-theoretic approach to critical phenomena takes place in the more complete Wilson theory of renormalization and qualitatively discuss its domain of validity. By the way, we suggest that the differential…

This PhD thesis is devoted to show that differential renormalization is a simple and useful renormalization method that we can use when dealing with gauge theories. In this work, it is shown how the one-loop results of Constraint…

Beginning with the conjecture of Artin and Tate in 1966, there has been a series of successively more general conjectures expressing the special values of the zeta function of an algebraic variety over a finite field in terms of other…

We elaborate notions of integration over the space of arcs factorized by the natural $C^*$-action and over the space of non-parametrized arcs (branches). There are offered two motivic versions of the zeta function of the classical monodromy…

We give an explicit formula of the coefficients of the Zeta-Function's L-polynomial for algebraic function fields over finite constant fields. Thus, we deduce an expression of the class number of algebraic function fields defined over…

We consider a self-interacting, massive rank-1 field coupled to quantum gravity. The theory is renormalizable by power counting and contains a massive spin-1 field and a massive scalar field. The latter has a propagator with negative…

This paper surveys a comprehensive, although not exhaustive, sampling of graph polynomials with the goal of providing a brief overview of a variety of techniques defining a graph polynomial and then for decoding the combinatorial…

We argue that in general renormalizable field theories the topological angles may develop an additive beta function starting no earlier than 2-loop order. The leading expression is uniquely determined by a single model-independent…

In this paper we define the triangulated category of motives over a simplicial scheme. The morphisms between the Tate objects in this category compute the motivic cohomology of the underlying scheme. In the last section we consider the…

We define reduced zeta functions of Lie algebras, which can be derived from motivic zeta functions using the Euler characteristic. We show that reduced zeta functions of Lie algebras possessing a suitably well-behaved basis are easy to…