• Corpus ID: 234482792

Algebraic Interplay between Renormalization and Monodromy

@inproceedings{Kreimer2021AlgebraicIB,
  title={Algebraic Interplay between Renormalization and Monodromy},
  author={Dirk Kreimer and Karen A. Yeats},
  year={2021}
}
We investigate combinatorial and algebraic aspects of the interplay between renormalization and monodromies for Feynman amplitudes. We clarify how extraction of subgraphs from a Feynman graph interacts with putting edges onshell or with contracting them to obtain reduced graphs. Graph by graph this leads to a study of cointeracting bialgebras. One bialgebra comes from extraction of subgraphs and hence is needed for renormalization. The other bialgebra is an incidence bialgebra for edges put… 
Pathlike Co/bialgebras and their antipodes with applications to bi- and Hopf algebras appearing in topology, number theory and physics
We develop an algebraic theory of flavored and pathlike co-, biand Hopf algebras. This is the right framework in which to discuss antipodes for bialgebras naturally appearing in topology, number
The diagrammatic coaction beyond one loop
Abstract The diagrammatic coaction maps any given Feynman graph into pairs of graphs and cut graphs such that, conjecturally, when these graphs are replaced by the corresponding Feynman integrals
Subdivergence-free gluings of trees
TLDR
The problem and language is motivated by quantum field theory, and enumerate subdivergence-free gluings for certain families of trees, showing a connection with connected permutations, and the algorithms to compute subdiversion-freegluings are given.
Local Unitarity: cutting raised propagators and localising renormalisation
The Local Unitarity (LU) representation of differential cross-sections locally realises the cancellations of infrared singularities predicted by the Kinoshita-Lee-Nauenberg theorem. In this work we

References

SHOWING 1-10 OF 85 REFERENCES
Graphs in perturbation theory
This thesis provides an extension of the work of Dirk Kreimer and Alain Connes on the Hopf algebra structure of Feynman graphs and renormalization to general graphs. Additionally, an algebraic
Invariant Differential Forms on Complexes of Graphs and Feynman Integrals
  • F. Brown
  • Mathematics
    Symmetry, Integrability and Geometry: Methods and Applications
  • 2021
We study differential forms on an algebraic compactification of a moduli space of metric graphs. Canonical examples of such forms are obtained by pulling back invariant differentials along a tropical
The Hopf algebra structure of the R∗-operation
We give a Hopf-algebraic formulation of the $R^*$-operation, which is a canonical way to render UV and IR divergent Euclidean Feynman diagrams finite. Our analysis uncovers a close connection to
Non-perturbative completion of Hopf-algebraic Dyson-Schwinger equations
Three Hopf algebras from number theory, physics & topology, and their common background I: operadic & simplicial aspects
We consider three a priori totally different setups for Hopf algebras from number theory, mathematical physics and algebraic topology. These are the Hopf algebra of Goncharov for multiple zeta
Renormalization of Gauge Fields: A Hopf Algebra Approach
We study the Connes–Kreimer Hopf algebra of renormalization in the case of gauge theories. We show that the Ward identities and the Slavnov–Taylor identities (in the abelian and non-abelian case
Anatomy of a gauge theory
CHROMATIC POLYNOMIALS AND BIALGEBRAS OF GRAPHS
  • L. Foissy
  • Mathematics
    International Electronic Journal of Algebra
  • 2021
The chromatic polynomial is characterized as the unique polynomial invariant of graphs, compatible with two interacting bialgebras structures: the first coproduct is given by partitions of vertices
...
...