Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

Special Issue on Algebraic Structures in Perturbative Quantum Field Theory in honor of Dirk Kreimer for his 60th birthday

The Guest Editors for this special issue are

Kurusch Ebrahimi-Fard (Norwegian University of Science and Technology, Norway)
Erik Panzer (University of Oxford, UK)
Karen Yeats (University of Waterloo, Canada)

This special issue is dedicated to Dirk Kreimer on the occasion of his 60th birthday.

Most of the papers in this special issue were also presented at the corresponding conference held at IHES in Bures-sur-Yvette, France, on November 16–20, 2020.

We wish to thank also all the authors who have published papers in the issue, and to give our special thanks to all the referees for providing constructive reports.

Guest Editors        

The editors gave me an opportunity to write a little note to share some memories and most importantly to express gratitude to the organizers, to the speakers and to the participants.

In organizing this conference the IHES and its staff, most notably Élisabeth Jasserand, have given proof once more of their overwhelming hospitality and support, pandemic conditions notwithstanding.

During my first visits to the IHES I came to it with ideas on knots and Feynman diagrams in mind. Eventually that led to a lifelong interest on the nature and rôle of periods in quantum field theory, an interest which owes substantially to sharing it with David Broadhurst. To see more clearly what was going on one had to dig those periods out of the computational complexities of renormalized Feynman diagram computations.

When this led to Hopf algebras and renormalization and a collaboration with Alain Connes, the affiliation to IHES became ever firmer. The IHES was a wonderful place then – and is today – through the excellence of the scientists who roam its floors, and equally important through the kindness of its staff.

Élisabeth and Cécile in the first floor of the scientific building, Patrick, chef of the caféteria and a man of unfailing humour and support for the hungry, as well as the IT support given by Francois Bachelier and Karim Ben Abdallah defined and define the spirit of this place. To all of them I owe thanks and gratitude in many ways.

Many of my scientific contacts were established here at IHES, and are reflected at this conference. So for me this workshop was a very happy reunion the more so as it was dedicated to the algebraic structure in locally interacting quantum field theories.

Let me close once more by thanking the organizers Karen Yeats, Erik Panzer and Élisabeth Jasserand, Kurusch Ebrahimi-Fard and all others who helped, the speakers and the participants once again.

Dirk Kreimer        

Papers in this Issue:

Pathlike Co/Bialgebras and their Antipodes with Applications to Bi- and Hopf Algebras Appearing in Topology, Number Theory and Physics
Ralph M. Kaufmann and Yang Mo
SIGMA 18 (2022), 053, 42 pages   [ abs   pdf ]
Clean Single-Valued Polylogarithms
Steven Charlton, Claude Duhr and Herbert Gangl
SIGMA 17 (2021), 107, 34 pages   [ abs   pdf ]
Invariant Differential Forms on Complexes of Graphs and Feynman Integrals
Francis Brown
SIGMA 17 (2021), 103, 54 pages   [ abs   pdf ]
The Algebraic Structure of the KLT Relations for Gauge and Gravity Tree Amplitudes
Hadleigh Frost
SIGMA 17 (2021), 101, 23 pages   [ abs   pdf ]
$c_2$ Invariants of Hourglass Chains via Quadratic Denominator Reduction
Oliver Schnetz and Karen Yeats
SIGMA 17 (2021), 100, 26 pages   [ abs   pdf ]
Renormalization in Combinatorially Non-Local Field Theories: the BPHZ Momentum Scheme
Johannes Thürigen
SIGMA 17 (2021), 094, 14 pages   [ abs   pdf ]
Semiclassical Trans-Series from the Perturbative Hopf-Algebraic Dyson-Schwinger Equations: $\phi^3$ QFT in 6 Dimensions
Michael Borinsky, Gerald V. Dunne and Max Meynig
SIGMA 17 (2021), 087, 26 pages   [ abs   pdf ]
Algebraic Structures on Typed Decorated Rooted Trees
Loïc Foissy
SIGMA 17 (2021), 086, 28 pages   [ abs   pdf ]
Perturbative and Geometric Analysis of the Quartic Kontsevich Model
Johannes Branahl, Alexander Hock and Raimar Wulkenhaar
SIGMA 17 (2021), 085, 33 pages   [ abs   pdf ]
Resurgent Analysis of Ward-Schwinger-Dyson Equations
Marc P. Bellon and Enrico I. Russo
SIGMA 17 (2021), 075, 18 pages   [ abs   pdf ]
New Techniques for Worldline Integration
James P. Edwards, C. Moctezuma Mata, Uwe Müller and Christian Schubert
SIGMA 17 (2021), 065, 19 pages   [ abs   pdf ]
Generalized Gross-Neveu Universality Class with Non-Abelian Symmetry
John A. Gracey
SIGMA 17 (2021), 064, 20 pages   [ abs   pdf ]
Double Box Motive
Spencer Bloch
SIGMA 17 (2021), 048, 12 pages   [ abs   pdf ]

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