Dirk Kreimer

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Dirk Kreimer is affiliated with the following schools: Humboldt University of Berlin, Boston University, University of Mainz, Durham University

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Dirk Kreimer

Physics

#5371

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#7195

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Physics

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According to Wikipedia, Dirk Kreimer is a German physicist who pioneered the Hopf-algebraic approach to perturbative quantum field theory with Alain Connes and other co-authors. He is currently Humboldt professor at the department of mathematics of Humboldt University in Berlin, where he teaches the courses of Quantum Field Theory and Hopf Algebras and the Renormalization Group.

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Dirk Kreimer's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Renormalization in Quantum Field Theory and the Riemann–Hilbert Problem I: The Hopf Algebra Structure of Graphs and the Main Theorem (1999) (798)
Hopf Algebras, Renormalization and Noncommutative Geometry (1998) (792)
Renormalization in Quantum Field Theory and the Riemann--Hilbert Problem II: The β-Function, Diffeomorphisms and the Renormalization Group (1999) (519)
On the Hopf algebra structure of perturbative quantum field theories (1997) (439)
Association of multiple zeta values with positive knots via Feynman diagrams up to 9 loops (1996) (314)
On Motives Associated to Graph Polynomials (2005) (237)
Chen’s iterated integral represents the operator product expansion (1999) (170)
Knots and Numbers in ϕ4 Theory to 7 Loops and Beyond (1995) (162)
Spitzer's identity and the algebraic Birkhoff decomposition in pQFT (2004) (154)
Anatomy of a gauge theory (2005) (135)
Knots and Feynman Diagrams (2000) (129)
Exact solutions of Dyson-Schwinger equations for iterated one-loop integrals and propagator-coupling duality (2000) (121)
On Overlapping Divergences (1998) (120)
Beyond the triangle and uniqueness relations: non-zeta counterterms at large N from positive knots (1996) (113)
An Étude in non-linear Dyson–Schwinger Equations ⁎ (2006) (108)
Mixed Hodge Structures and Renormalization in Physics (2008) (95)
Hopf algebras in renormalization theory: Locality and Dyson-Schwinger equations from Hochschild cohomology (2005) (93)
A practicableγ5-scheme in dimensional regularization (1992) (93)
Angles, Scales and Parametric Renormalization (2011) (88)
Combinatorics of (perturbative) quantum field theory (2000) (85)
Renormalization Automated by Hopf Algebra (1998) (74)
Insertion and Elimination: the Doubly Infinite Lie Algebra of Feynman Graphs (2002) (68)
The γ5-problem and anomalies — A Clifford algebra approach (1990) (66)
Combinatoric explosion of renormalization tamed by Hopf algebra: 30-loop Padé-Borel resummation (1999) (65)
Unknotting the polarized vacuum of quenched QED (1996) (55)
Structures in Feynman Graphs -Hopf Algebras and Symmetries (2002) (54)
Feynman amplitudes and Landau singularities for 1-loop graphs (2010) (54)
The master two-loop two-point function. The general case (1991) (51)
Towards Cohomology of Renormalization: Bigrading the Combinatorial Hopf Algebra of Rooted Trees (2000) (50)
A remark on quantum gravity (2007) (47)
Recursive relations in the core Hopf algebra (2009) (46)
Integrable Renormalization II: The General Case (2004) (46)
Quantization of gauge fields, graph polynomials and graph homology (2012) (45)
Comment on ``Topological invariants, instantons, and the chiral anomaly on spaces with torsion'' (1999) (45)
Dyson Schwinger Equations: From Hopf algebras to Number Theory (2006) (44)
Using the Hopf Algebra Structure of QFT in Calculations (1999) (44)
The Hopf Algebra of Rooted Trees in Epstein-Glaser Renormalization (2004) (42)
New mathematical structures in renormalizable quantum field theories (2002) (40)
Universality and Renormalization: From Stochastic Evolution to Renormalization of Quantum Fields (2007) (37)
The QCD β-function from global solutions to Dyson–Schwinger equations (2008) (37)
The core Hopf algebra (2009) (37)
Factorization in Quantum Field Theory: An Exercise in Hopf Algebras and Local Singularities (2003) (36)
Renormalization and Knot Theory (1994) (33)
Cutkosky Rules and Outer Space (2015) (33)
TOPICAL REVIEW: The Hopf algebra approach to Feynman diagram calculations (2005) (33)
Integrable renormalization I: The ladder case (2004) (31)
Recursion and Growth Estimates in Renormalizable Quantum Field Theory (2006) (31)
New representation of two-loop propagator and vertex functions (1994) (31)
Renormalization and Mellin Transforms (2012) (30)
Scientific Advisory Committee (2014) (28)
MOTIVES ASSOCIATED TO GRAPHS (2006) (28)
Combinatorial Dyson-Schwinger equations in noncommutative field theory (2009) (27)
The residues of quantum field theory - numbers we should know (2004) (25)
RENORMALIZATION AND RESOLUTION OF SINGULARITIES (2009) (25)
The Structure of the Ladder Insertion-Elimination Lie Algebra (2004) (24)
Insertion and Elimination Lie Algebra: The Ladder Case (2003) (24)
The two-loop three-point functions: general massive cases (1992) (23)
Resummation of infrared logarithms in de Sitter space via Dyson-Schwinger equations: The ladder-rainbow approximation (2013) (23)
Knots and divergences (1995) (22)
Filtrations in Dyson-Schwinger equations: next-to^{j} -leading log expansions systematically (2014) (21)
Étude for linear Dyson – Schwinger Equations (21)
The QCD beta-function from global solutions to Dyson-Schwinger equations (2009) (20)
The Role of $\gamma_5$ in Dimensional Regularization (1994) (20)
On the Brownian gas: a field theory with a Poissonian ground state (2008) (20)
Shuffling Quantum Field Theory (1999) (19)
Properties of the Corolla Polynomial of a 3-regular Graph (2012) (19)
Diagrammatic Cancellations and the Gauge Dependence of QED (2016) (17)
On the invariance of residues of Feynman graphs (2001) (17)
Chiral Anomaly in Contorted Spacetimes (1999) (16)
Feynman diagrams as a weight system: four-loop test of a four-term relation 1 Work supported in part (1996) (15)
One loop integrals revisited (1992) (15)
Self-consistency of off-shell Slavnov-Taylor identities in QCD (2019) (15)
What is the trouble with Dyson–Schwinger equations? (2004) (15)
CHIRAL ANOMALY IN ASHTEKAR'S APPROACH TO CANONICAL GRAVITY (1998) (15)
New representation of the two-loop crossed vertex function (1996) (14)
Calculation of infrared-divergent Feynman diagrams with zero mass threshold (1997) (13)
Unique factorization in perturbative QFT (2003) (13)
Not so Non-Renormalizable Gravity (2008) (13)
Diffeomorphisms of Quantum Fields (2016) (12)
Cutkosky Rules from Outer Space (2016) (12)
Weight Systems from Feynman Diagrams (1996) (12)
Outer Space as a Combinatorial Backbone for Cutkosky Rules and Coactions (2020) (12)
xloops — automated Feynman diagram calculation (1998) (12)
Lessons from Quantum Field Theory (1999) (11)
From Local Perturbation Theory to Hopf and Lie Algebras of Feynman Graphs (2001) (11)
Algebraic Interplay between Renormalization and Monodromy (2021) (10)
On knots in subdivergent diagrams (1996) (10)
Quantum fields, periods and algebraic geometry (2014) (10)
Multi-valued Feynman Graphs and Scattering Theory (2018) (9)
Algebraic Structures in local QFT (2010) (9)
Avoidance of a Landau pole by flat contributions in QED (2013) (9)
TENSOR INTEGRALS FOR TWO-LOOP STANDARD MODEL CALCULATIONS (1993) (9)
The next-to-ladder approximation for linear Dyson Schwinger equations (2006) (9)
How useful can knot and number theory be for loop calculations (1998) (9)
LOOP INTEGRALS, ℛ-FUNCTIONS AND THEIR ANALYTIC CONTINUATION (1993) (9)
Field Diffeomorphisms and the Algebraic Structure of Perturbative Expansions (2012) (9)
The corolla polynomial: a graph polynomial on half-edges (2018) (8)
A short note on two-loop box functions (1994) (8)
ONE-LOOP INTEGRALS REVISITED — THE THREE-POINT FUNCTIONS (1993) (8)
Feynman diagrams and polylograithms: shuffles and pentagons (2000) (7)
Decomposing Feynman rules (2012) (7)
Introduction to XLOOPS (1996) (7)
New algebraic aspects of perturbative and non-perturbative Quantum Field Theory (2007) (7)
Bananas: multi-edge graphs and their Feynman integrals (2022) (7)
THE NEXT-TO-LADDER APPROXIMATION FOR DYSON-SCHWINGER EQUATIONS (2006) (7)
Graph complexes and Feynman rules (2020) (7)
oneloop 2.0 — A program package calculating one-loop integrals (1997) (6)
ON THE INSERTION-ELIMINATION LIE ALGEBRA OF FEYNMAN GRAPHS (2004) (5)
Hopf Algebra Structure of Renormalizable Quantum Field Theory (2006) (5)
Renormalization & Renormalization Group (2013) (5)
The methods of XLOOPS An introduction to parallel space techniques (1997) (5)
First results with a new method for calculating 2-loop box-functions (1998) (4)
On Feynman graphs as elements of a Hopf algebra (1999) (4)
Choice of the alumina-feldspar ratio in high-strength porcelain bodies (1990) (4)
What can we learn from Knizhnik--Zamolodchikov Equations? (2014) (3)
10 02 2 v 1 3 O ct 1 99 8 On Overlapping Divergences (1999) (3)
Xloops: A Program package calculating one loop and two loop Feynman diagrams (1997) (3)
Combinatorial BRST homology and graph differentials (2017) (3)
Tensor structure from scalar Feynman matroids (2010) (3)
Erratum to “New mathematical structures in renormalizable quantum field theories” [Ann. Physics 303 (2003) 179–202] (2003) (2)
The QED β-function from global solutions to Dyson-Schwinger equations (2021) (2)
Influence of phase composition of aluminous porcelain on its mechanical strength (1989) (2)
Feynman Diagram Calculations - From finite Integral Representations to knotted Infinities (1995) (2)
On wind-influenced sound propagation (1992) (2)
Feynman diagrams and their algebraic lattices (2015) (1)
Algebra for quantum fields (2009) (1)
Wonderful Renormalization (2014) (1)
Locality, QED and classical electrodynamics (1998) (1)
An algebraic approach to Z-Factors (1994) (1)
2-loop Integrals in the Standard Model (1992) (1)
Feynman integrals and hyperlogarithms (2015) (0)
SUMMER SCHOOL “THE STRUCTURE OF LOCAL QUANTUM FIELDS” ORGS.: DIRK KREIMER WITH SPENCER BLOCH AND FRANCIS BROWN (2009) (0)
Algebras for quantum fields (0)
From Tasmania with Love (2008) (0)
REDUCTION RELATIONS FOR FEYNMAN INTEGRALS VIA PARAMETRIC ANNIHILATORS Submitted (2016) (0)
Quantization of gauge fi elds , graph polynomials and graph homology 1 (2021) (0)
2 2 6 N ov 2 00 2 New mathematical structures in renormalizable quantum field theories ∗ (2008) (0)
Knots and Feynman Diagrams: Knots and transcendentals (2000) (0)
O ct 2 00 0 Combinatorics of ( perturbative ) Quantum Field Theory (2000) (0)
Dyson–Schwinger equations: Fix-point equations for quantum fields (2018) (0)
Knots to numbers: (2, 2n – 3) torus knots and ζ(2n – 3) (2000) (0)
D ec 2 01 5 CUTKOSKY RULES AND OUTER SPACE (2015) (0)
Angles, Scales and Parametric Renormalization (2013) (0)
Knots and Feynman Diagrams: The simplest link diagrams (2000) (0)
P o S ( L L 2 0 1 6 ) 0 3 5 Cutkosky Rules from Outer Space (2016) (0)
Filtrations in Dyson-Schwinger equations (2013) (0)
Knots and Feynman Diagrams: Euler–Zagier sums (2000) (0)
Knots and Feynman Diagrams: References (2000) (0)
Se p 20 05 Anatomy of a gauge theory (2006) (0)
Rationality: no knots, no transcendentals (2000) (0)
The four-term relation (2000) (0)
Field Diffeomorphisms and the Algebraic Structure of Perturbative Expansions (2012) (0)
Necessary topics from knot theory (2000) (0)
Knots and Feynman Diagrams: One-loop words (2000) (0)
2 Fe b 19 99 On Overlapping Divergences (1999) (0)
Knots and Feynman Diagrams: The Hopf algebra structure of renormalization (2000) (0)
calculating One-Loop Integrals (1997) (0)
A ug 2 00 9 RENORMALIZATION AND RESOLUTION OF SINGULARITIES (2009) (0)
Locality, QED and classical electrodynamics (1998) (0)
Matilde Marcolli: Feynman Motives (2012) (0)
COMBINATORIAL AND GEOMETRIC ASPECTS OF FEYNMAN GRAPHS AND FEYNMAN INTEGRALS DISSERTATION (2009) (0)
12 29 0 v 1 3 1 D ec 1 99 9 Shuffling Quantum Field Theory ∗ (2008) (0)
Diffeomorphisms of Quantum Fields (2017) (0)
12 29 0 v 3 3 A pr 2 00 0 Shuffling Quantum Field Theory ∗ (2008) (0)
Knots and Feynman Diagrams: Perturbative quantum field theory (2000) (0)
Three Etudes in QFT (2009) (0)
Institute for Mathematical Physics Combinatoric Explosion of Renormalization Tamed by Hopf Algebra: 30{loop Pad E{borel Resummation Combinatoric Explosion of Renormalization Tamed by Hopf Algebra: 30-loop Pad E-borel Resummation (1999) (0)
Moduli Spaces of Gluon Graphs (2019) (0)
Recursive Relations in the Core Hopf Algebra Dirk Kreimer (2009) (0)
Hopf algebras, non-commutative geometry, and what else? (2000) (0)
P o S ( L L 2 0 1 2 ) 0 4 9 Decomposing Feynman rules (2012) (0)
N ov 2 00 2 New mathematical structures in renormalizable quantum field theories ∗ (2008) (0)
Institute for Mathematical Physics Renormalization Automated by Hopf Algebra Renormalization Automated by Hopf Algebra (2009) (0)
Chiral Anomaly in Contorted Spacetimes Typeset Using Revt E X (1997) (0)

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What Schools Are Affiliated With Dirk Kreimer?

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