Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 2019, Volume 52, Issue 4, p. 45401

Based on general mathematical assumptions we give an independent, elementary derivation of a theorem by Brown and Dupont (2018 Talk given by F Brown in 'String...

string amplitudes | multiple zeta values | number theory | POLYLOGARITHMS | INTEGRALS | PHYSICS, MULTIDISCIPLINARY | AMPLITUDES | PHYSICS, MATHEMATICAL

string amplitudes | multiple zeta values | number theory | POLYLOGARITHMS | INTEGRALS | PHYSICS, MULTIDISCIPLINARY | AMPLITUDES | PHYSICS, MATHEMATICAL

Journal Article

Communications in Number Theory and Physics, ISSN 1931-4523, 2014, Volume 8, Issue 4, pp. 589 - 675

Graphical functions are single-valued complex functions which arise from Feynman amplitudes. We study their properties and use their connection to multiple...

MATHEMATICS, APPLIED | NUMBERS | ALGEBRA | QUANTUM-FIELD THEORY | PHYSICS, MATHEMATICAL | INTEGRALS | PHI | MATHEMATICS | DIMENSIONS | FEYNMAN DIAGRAMS | ZETA VALUES | LOOPS | MOTIVES

MATHEMATICS, APPLIED | NUMBERS | ALGEBRA | QUANTUM-FIELD THEORY | PHYSICS, MATHEMATICAL | INTEGRALS | PHI | MATHEMATICS | DIMENSIONS | FEYNMAN DIAGRAMS | ZETA VALUES | LOOPS | MOTIVES

Journal Article

Duke Mathematical Journal, ISSN 0012-7094, 2012, Volume 161, Issue 10, pp. 1817 - 1862

Journal Article

Communications in Number Theory and Physics, ISSN 1931-4523, 2018, Volume 12, Issue 2, pp. 335 - 354

Recently S. Laporta published a partial result on the fourth order QED contribution to the electron anomalous magnetic moment g - 2 [17]. This result contains...

MIXED TATE MOTIVES | MATHEMATICS | MATHEMATICS, APPLIED | PERIODS | FUNDAMENTAL-GROUPS | UNITY | ROOTS | MULTIPLE POLYLOGARITHM VALUES | PHYSICS, MATHEMATICAL

MIXED TATE MOTIVES | MATHEMATICS | MATHEMATICS, APPLIED | PERIODS | FUNDAMENTAL-GROUPS | UNITY | ROOTS | MULTIPLE POLYLOGARITHM VALUES | PHYSICS, MATHEMATICAL

Journal Article

Communications in Number Theory and Physics, ISSN 1931-4523, 2010, Volume 4, Issue 1, pp. 1 - 47

Journal Article

Physical Review D, ISSN 2470-0010, 04/2018, Volume 97, Issue 8

We review recent results in the theory of numbers and single-valued functions on the complex plane which arise in quantum field theory. These results are the...

INTEGRALS | PERIODS | ASTRONOMY & ASTROPHYSICS | VALUED MULTIPLE POLYLOGARITHMS | GRAPHICAL FUNCTIONS | ELECTRON G-2 | C INVARIANTS | MASSLESS PROPAGATORS | MOTIVES | COACTION | PHYSICS, PARTICLES & FIELDS | Mathematical Physics | High Energy Physics - Theory | Mathematics - Number Theory

INTEGRALS | PERIODS | ASTRONOMY & ASTROPHYSICS | VALUED MULTIPLE POLYLOGARITHMS | GRAPHICAL FUNCTIONS | ELECTRON G-2 | C INVARIANTS | MASSLESS PROPAGATORS | MOTIVES | COACTION | PHYSICS, PARTICLES & FIELDS | Mathematical Physics | High Energy Physics - Theory | Mathematics - Number Theory

Journal Article

Letters in Mathematical Physics, ISSN 0377-9017, 06/2017, Volume 107, Issue 6, pp. 1177 - 1192

Graphical functions are positive functions on the punctured complex plane which arise in quantum field theory. We generalize a parametric integral...

Feynman integrals | Perturbation theory | Graphical functions | Parametric representation | POLYNOMIALS | FEYNMAN-INTEGRALS | THEOREM | VALUED MULTIPLE POLYLOGARITHMS | PROOF | PHYSICS, MATHEMATICAL

Feynman integrals | Perturbation theory | Graphical functions | Parametric representation | POLYNOMIALS | FEYNMAN-INTEGRALS | THEOREM | VALUED MULTIPLE POLYLOGARITHMS | PROOF | PHYSICS, MATHEMATICAL

Journal Article

Physical Review. D, Covering Particles, Fields, Gravitation and Cosmology, ISSN 2470-0010, 04/2018, Volume 97, Issue 8, p. 085018

We review recent results in the theory of numbers and single-valued functions on the complex plane which arise in quantum field theory. These results are the...

Subtraction | Field theory | Quantum field theory | Quantum theory

Subtraction | Field theory | Quantum field theory | Quantum theory

Journal Article

Electronic Journal of Combinatorics, ISSN 1077-8926, 2011, Volume 18, Issue 1

We consider the number (N) over bar (q) of points in the projective complement of graph hypersurfaces over F-q and show that the smallest graphs with...

MATHEMATICS | MATHEMATICS, APPLIED | MOTIVES

MATHEMATICS | MATHEMATICS, APPLIED | MOTIVES

Journal Article

DUKE MATHEMATICAL JOURNAL, ISSN 0012-7094, 07/2012, Volume 161, Issue 10, pp. 1817 - 1862

Inspired by Feynman integral computations in quantum field theory, Kontsevich conjectured in 1997 that the number of points of graph hypersurfaces over a...

POLYNOMIALS | MATHEMATICS | FEYNMAN GRAPHS | MOTIVES | 14M12 | 14G10 | 11G25 | 05A15 | 81T18

POLYNOMIALS | MATHEMATICS | FEYNMAN GRAPHS | MOTIVES | 14M12 | 14G10 | 11G25 | 05A15 | 81T18

Journal Article

The Electronic Journal of Combinatorics, ISSN 1077-8926, 05/2011, Volume 18, Issue 1

We consider the number $\bar N(q)$ of points in the projective complement of graph hypersurfaces over $\mathbb{F}_q$ and show that the smallest graphs with...

Journal Article

Advances in Theoretical and Mathematical Physics, ISSN 1095-0761, 2014, Volume 18, Issue 2, pp. 323 - 362

Journal Article

Annals of Physics, ISSN 0003-4916, 2006, Volume 321, Issue 11, pp. 2604 - 2637

The massive Gross–Neveu model is solved in the large- N limit at finite temperature and chemical potential. The scalar potential is given in terms of Jacobi...

BIPOLARON LATTICE | INSTABILITY | SYMMETRY | POLARONS | TEMPERATURE | PHYSICS, MULTIDISCIPLINARY | FIELD | BAND | CONDUCTING POLYMERS | Temperature | Models | Polymers | Diagrams | Phase transitions | Physics | CRYSTAL MODELS | POLYMERS | PHYSICS OF ELEMENTARY PARTICLES AND FIELDS | PHASE DIAGRAMS | SCALARS | JACOBIAN FUNCTION | MASS | CRYSTALS | EQUATIONS | QUARKS | POTENTIALS | PHASE TRANSFORMATIONS

BIPOLARON LATTICE | INSTABILITY | SYMMETRY | POLARONS | TEMPERATURE | PHYSICS, MULTIDISCIPLINARY | FIELD | BAND | CONDUCTING POLYMERS | Temperature | Models | Polymers | Diagrams | Phase transitions | Physics | CRYSTAL MODELS | POLYMERS | PHYSICS OF ELEMENTARY PARTICLES AND FIELDS | PHASE DIAGRAMS | SCALARS | JACOBIAN FUNCTION | MASS | CRYSTALS | EQUATIONS | QUARKS | POTENTIALS | PHASE TRANSFORMATIONS

Journal Article

Journal of Number Theory, ISSN 0022-314X, 03/2015, Volume 148, pp. 478 - 506

A long-standing conjecture in quantum field theory due to Broadhurst and Kreimer states that the periods of the zig–zag graphs are a certain explicit rational...

Multiple zeta values | Quantum field theory | Single-valued polylogarithms | DIAGRAMS | MATHEMATICS | DIMENSIONS | NUMBERS | ALGEBRA | LOOPS | MOTIVES

Multiple zeta values | Quantum field theory | Single-valued polylogarithms | DIAGRAMS | MATHEMATICS | DIMENSIONS | NUMBERS | ALGEBRA | LOOPS | MOTIVES

Journal Article

Physical Review Letters, ISSN 0031-9007, 04/2008, Volume 100, Issue 16, p. 160601

Based on the study of saddle points of the potential energy landscapes of generic classical many-particle systems, we present a necessary criterion for the...

CONFIGURATION-SPACE | TOPOLOGY | FERROMAGNETISM | PHYSICS, MULTIDISCIPLINARY

CONFIGURATION-SPACE | TOPOLOGY | FERROMAGNETISM | PHYSICS, MULTIDISCIPLINARY

Journal Article

Advances in Theoretical and Mathematical Physics, ISSN 1095-0761, 2014, Volume 18, Issue 2, pp. 323 - 362

The c_2 invariant of a Feynman graph is an arithmetic invariant which detects many properties of the corresponding Feynman integral. In this paper, we define...

Journal Article

Communications in Number Theory and Physics, ISSN 1931-4523, 2013, Volume 7, Issue 2, pp. 293 - 325

The amplitude of a Feynman graph in Quantum Field Theory is related to the point-count over finite fields of the corresponding graph hypersurface. This article...

POLYNOMIALS | MATHEMATICS | MATHEMATICS, APPLIED | PHYSICS, MATHEMATICAL | MOTIVES

POLYNOMIALS | MATHEMATICS | MATHEMATICS, APPLIED | PHYSICS, MATHEMATICAL | MOTIVES

Journal Article

05/2019

In perturbative quantum field theory one encounters certain, very specific geometries over the integers. These `perturbative quantum geometries' determine the...

Journal Article

08/2018

Based on general mathematical assumptions we give an independent, elementary derivation of a theorem by Francis Brown and Cl\'ement Dupont which states that...

Journal Article

Communications in Number Theory and Physics, ISSN 1931-4523, 2017, Volume 11, Issue 3, pp. 657 - 705

Journal Article

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