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Nuclear Physics, Section B, ISSN 0550-3213, 03/2014, Volume 880, Issue 1, pp. 343 - 377
A new class of identities for Feynman graph amplitudes, dubbed Schouten identities, valid at fixed integer value of the dimension d is proposed. The identities... 
Multi-loop calculations | Schouten identities | Feynman graphs | NUMERICAL EVALUATION | PHYSICS, PARTICLES & FIELDS | Physics - High Energy Physics - Phenomenology
Journal Article
International Journal of Modern Physics A, ISSN 0217-751X, 05/2010, Volume 25, Issue 13, pp. 2585 - 2618
The integrand of any multiloop integral is characterized after Feynman parametrization by two polynomials. In this review we summarize the properties of these... 
Feynman integrals | Graphs | Perturbative calculations | graphs | EXPANSIONS | PHYSICS, NUCLEAR | MOTIVES | PHYSICS, PARTICLES & FIELDS
Journal Article
Journal of Number Theory, ISSN 0022-314X, 03/2015, Volume 148, pp. 328 - 364
We study the sunset graph defined as the scalar two-point self-energy at two-loop order. We evaluated the sunset integral for all identical internal masses in... 
Motives | Elliptic dilogarithm | Eisenstein series | Feynman graph | Variation of mixed hodge structures | DIAGRAMS | MATHEMATICS | ONE-LOOP AMPLITUDES | DIFFERENTIAL-EQUATIONS | 2-LOOP
Journal Article
Journal of High Energy Physics, ISSN 1126-6708, 05/2017, Volume 2017, Issue 5, pp. 1 - 38
Journal Article
Journal of High Energy Physics, ISSN 1029-8479, 9/2019, Volume 2019, Issue 9, pp. 1 - 33
Journal Article
Journal of High Energy Physics, ISSN 1029-8479, 4/2019, Volume 2019, Issue 4, pp. 1 - 73
Journal Article
Journal of Mathematical Physics, ISSN 0022-2488, 05/2013, Volume 54, Issue 5, p. 52303
We discuss the analytical solution of the two-loop sunrise graph with arbitrary non-zero masses in two space-time dimensions. The analytical result is obtained... 
INTEGRALS | SPACE | CONNECTION | FEYNMAN DIAGRAMS | DIFFERENTIAL-EQUATIONS | THRESHOLD EXPANSION | MASTER AMPLITUDES | NUMERICAL EVALUATION | PHYSICS, MATHEMATICAL | SUNSET DIAGRAM | SELF-ENERGIES | Graphs | Sunrise | Mathematical analysis | Differential equations | Elliptic integrals | Physics - High Energy Physics - Phenomenology
Journal Article
Annals of Physics, ISSN 0003-4916, 09/2013, Volume 336, pp. 180 - 222
We review quantization of gauge fields using algebraic properties of 3-regular graphs. We derive the Feynman integrand at n loops for a non-abelian gauge... 
Covariant quantization | Graph homology | Gauge theory | HOPF ALGEBRA | SPIN | PHYSICS, MULTIDISCIPLINARY | FEYNMAN-RULES | RENORMALIZATION | Graphs | Polynomials | Physics | Algebra | Quantization | Scalars | Gages | Gauges | POLYNOMIALS | REVIEWS | PHYSICS OF ELEMENTARY PARTICLES AND FIELDS | QUANTIZATION | SCALAR FIELDS | GRAPH THEORY
Journal Article
Journal Article
Advances in Theoretical and Mathematical Physics, ISSN 1095-0761, 2018, Volume 22, Issue 2, pp. 395 - 427
We study the dual graph polynomials phi(G) and the case when a Feynman graph has no triangles but has a 4-face. This leads to the proof of the duality... 
C INVARIANTS | FEYNMAN GRAPHS | PHYSICS, MATHEMATICAL | PHYSICS, PARTICLES & FIELDS
Journal Article
Journal of High Energy Physics, ISSN 1126-6708, 03/2018, Volume 2018, Issue 3, pp. 1 - 42
We consider a special double scaling limit, recently introduced by two of the authors, combining weak coupling and large imaginary twist, for the gamma-twisted... 
Conformal Field Theory | Integrable Field Theories | DUALITY | OPERATORS | PHYSICS, PARTICLES & FIELDS | Operators | Fermions | Scalars | Graphs | Correlators | Feynman diagrams | Three dimensional models
Journal Article
Computer Physics Communications, ISSN 0010-4655, 12/2014, Volume 185, Issue 12, pp. 3317 - 3330
Two programs for the computation of perturbative expansions of quantum field theory amplitudes are provided. feyngen can be used to generate Feynman graphs for... 
Feynman graphs | Renormalization | Hopf algebra | Feynman diagrams | Quantum field theory | BPHZ | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | GAUGE-FIELDS | PHYSICS, MATHEMATICAL | Analysis | Algebra | Legs | Mathematical analysis | Graphs | Summaries | Quantum theory | Programming languages | Combinatorial analysis
Journal Article
Journal of High Energy Physics, ISSN 1126-6708, 1/2019, Volume 2019, Issue 1, pp. 1 - 76
Journal Article
Annals of Physics, ISSN 0003-4916, 10/2017, Volume 385, pp. 328 - 346
In recent years enormous progress has been made in perturbative quantum field theory by applying methods of algebraic geometry to parametric Feynman integrals... 
Graph polynomial | Feynman integral | Quantum electrodynamics | PHYSICS, MULTIDISCIPLINARY | RENORMALIZATION | Atoms | Analysis
Journal Article
Journal of High Energy Physics, ISSN 1126-6708, 11/2017, Volume 2017, Issue 11, pp. 1 - 38
Journal Article