Journal of High Energy Physics, ISSN 1126-6708, 9/2017, Volume 2017, Issue 9, pp. 1 - 38

The low-energy expansion of one-loop amplitudes in type II string theory generates a series of world-sheet integrals whose integrands can be represented by...

Supersymmetric Effective Theories | M-Theory | Superstrings and Heterotic Strings | Quantum Physics | Conformal Field Models in String Theory | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | EISENSTEIN SERIES | INVARIANTS | PURE SPINOR | AMPLITUDE | STRING THEORY | DIMENSIONS | ONE-LOOP | EXPANSION | 2-LOOP SUPERSTRINGS | MULTIPLE ZETA VALUES | PHYSICS, PARTICLES & FIELDS | Analysis | Nuclear physics | String theory | Operators (mathematics) | Eigenvalues | Amplitudes | Feynman diagrams | Modular structures

Supersymmetric Effective Theories | M-Theory | Superstrings and Heterotic Strings | Quantum Physics | Conformal Field Models in String Theory | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | EISENSTEIN SERIES | INVARIANTS | PURE SPINOR | AMPLITUDE | STRING THEORY | DIMENSIONS | ONE-LOOP | EXPANSION | 2-LOOP SUPERSTRINGS | MULTIPLE ZETA VALUES | PHYSICS, PARTICLES & FIELDS | Analysis | Nuclear physics | String theory | Operators (mathematics) | Eigenvalues | Amplitudes | Feynman diagrams | Modular structures

Journal Article

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

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

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

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

The R*-operation by Chetyrkin, Tkachov, and Smirnov is a generalisation of the BPHZ R-operation, which subtracts both ultraviolet and infrared divergences of...

Renormalization Group | Perturbative QCD | DIFFERENTIAL-EQUATIONS | STAR-OPERATION | RENORMALIZATION-GROUP FUNCTIONS | PHYSICS, PARTICLES & FIELDS | Graphs | Infrared radiation | Tensors | Ultraviolet radiation | Divergence | Feynman diagrams | Nuclear and particle physics. Atomic energy. Radioactivity | High Energy Physics - Phenomenology | High Energy Physics - Theory

Renormalization Group | Perturbative QCD | DIFFERENTIAL-EQUATIONS | STAR-OPERATION | RENORMALIZATION-GROUP FUNCTIONS | PHYSICS, PARTICLES & FIELDS | Graphs | Infrared radiation | Tensors | Ultraviolet radiation | Divergence | Feynman diagrams | Nuclear and particle physics. Atomic energy. Radioactivity | High Energy Physics - Phenomenology | High Energy Physics - Theory

Journal Article

Journal of High Energy Physics, ISSN 1029-8479, 9/2019, Volume 2019, Issue 9, pp. 1 - 33

We present fully analytic results for all master integrals for the three-loop banana graph with four equal and non-zero masses. The results are remarkably...

NLO Computations | QCD Phenomenology | Quantum Physics | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | DIFFERENTIAL-EQUATIONS METHOD | FEYNMAN-INTEGRALS | ITERATED INTEGRALS | BOX | SUNRISE GRAPH | MASTER INTEGRALS | DIAGRAM | CONTINUATION | MODULAR-FORMS | PHYSICS, PARTICLES & FIELDS | Sunrise | Integrals | Subgroups | Exact solutions

NLO Computations | QCD Phenomenology | Quantum Physics | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | DIFFERENTIAL-EQUATIONS METHOD | FEYNMAN-INTEGRALS | ITERATED INTEGRALS | BOX | SUNRISE GRAPH | MASTER INTEGRALS | DIAGRAM | CONTINUATION | MODULAR-FORMS | PHYSICS, PARTICLES & FIELDS | Sunrise | Integrals | Subgroups | Exact solutions

Journal Article

Journal of High Energy Physics, ISSN 1029-8479, 4/2019, Volume 2019, Issue 4, pp. 1 - 73

Modular graph functions are SL(2, ℤ)-invariant functions associated with Feynman graphs of a two-dimensional conformal field theory on a torus of modulus τ....

Scattering Amplitudes | Superstrings and Heterotic Strings | Quantum Physics | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | COEFFICIENTS | VALUES | INVARIANTS | PHYSICS, PARTICLES & FIELDS | Astronomy | Algorithms | Lower bounds | Toruses | Mathematical analysis | Graphs | Field theory | Graph theory | Feynman diagrams | Fourier series

Scattering Amplitudes | Superstrings and Heterotic Strings | Quantum Physics | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | COEFFICIENTS | VALUES | INVARIANTS | PHYSICS, PARTICLES & FIELDS | Astronomy | Algorithms | Lower bounds | Toruses | Mathematical analysis | Graphs | Field theory | Graph theory | Feynman diagrams | Fourier series

Journal Article

2014, ISBN 9789814415873, xiv, 266

Book

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

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

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 of High Energy Physics, ISSN 1126-6708, 10/2016, Volume 2016, Issue 10, pp. 1 - 34

Recently, we proposed a new approach using a punctured Elliptic curve in the CHY framework in order to compute one-loop scattering amplitudes. In this note, we...

Scattering Amplitudes | Quantum Physics | Differential and Algebraic Geometry | Field Theories in Higher Dimensions | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | Differentialand Algebraic Geometry | PHYSICS, PARTICLES & FIELDS | Connectors | Construction | Computation | Ingredients | Scattering amplitude | Texts | Scalars | Feynman diagrams | Mathematical Physics | Nuclear and High Energy Physics | High Energy Physics - Theory

Scattering Amplitudes | Quantum Physics | Differential and Algebraic Geometry | Field Theories in Higher Dimensions | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | Differentialand Algebraic Geometry | PHYSICS, PARTICLES & FIELDS | Connectors | Construction | Computation | Ingredients | Scattering amplitude | Texts | Scalars | Feynman diagrams | Mathematical Physics | Nuclear and High Energy Physics | High Energy Physics - Theory

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

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

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

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

15.
Full Text
Heterotic-string amplitudes at one loop: modular graph forms and relations to open strings

Journal of High Energy Physics, ISSN 1126-6708, 1/2019, Volume 2019, Issue 1, pp. 1 - 76

We investigate one-loop four-point scattering of non-abelian gauge bosons in heterotic string theory and identify new connections with the corresponding...

Supergravity Models | Scattering Amplitudes | Superstrings and Heterotic Strings | Quantum Physics | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | BORN-INFELD ACTION | FEYNMAN-INTEGRALS | PERIODS | DIFFERENTIAL-EQUATIONS | DUALITY | MULTIPLE ZETA VALUES | PHYSICS, PARTICLES & FIELDS | String theory | Low energy | Toruses | Amplitudes | Integrals | Strings | Cylinders | Bosons

Supergravity Models | Scattering Amplitudes | Superstrings and Heterotic Strings | Quantum Physics | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | BORN-INFELD ACTION | FEYNMAN-INTEGRALS | PERIODS | DIFFERENTIAL-EQUATIONS | DUALITY | MULTIPLE ZETA VALUES | PHYSICS, PARTICLES & FIELDS | String theory | Low energy | Toruses | Amplitudes | Integrals | Strings | Cylinders | Bosons

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

Graph polynomial | Feynman integral | Quantum electrodynamics | PHYSICS, MULTIDISCIPLINARY | RENORMALIZATION | Atoms | Analysis

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 1993, Volume 105, Issue 2, pp. 279 - 289

A general method is devised for the automatic generation of Feynman diagrams in gauge (and other) field theories. The performance of an implemented computer...

PHYSICS, MATHEMATICAL | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | AMPLITUDES | PHYSICS OF ELEMENTARY PARTICLES AND FIELDS | ELECTRODYNAMICS | MATHEMATICAL MODELS | 990200 -- Mathematics & Computers | FEYNMAN DIAGRAM | QUANTUM ELECTRODYNAMICS | ALGORITHMS | COMPUTERIZED SIMULATION | FEASIBILITY STUDIES | FIELD THEORIES | DIAGRAMS | GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE | HIGH ENERGY PHYSICS | PHYSICS | MATHEMATICAL LOGIC | UNIFIED GAUGE MODELS | QUANTUM FIELD THEORY | PARTICLE MODELS | SIMULATION 662100 -- General Theory of Particles & Fields-- (1992-)

PHYSICS, MATHEMATICAL | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | AMPLITUDES | PHYSICS OF ELEMENTARY PARTICLES AND FIELDS | ELECTRODYNAMICS | MATHEMATICAL MODELS | 990200 -- Mathematics & Computers | FEYNMAN DIAGRAM | QUANTUM ELECTRODYNAMICS | ALGORITHMS | COMPUTERIZED SIMULATION | FEASIBILITY STUDIES | FIELD THEORIES | DIAGRAMS | GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE | HIGH ENERGY PHYSICS | PHYSICS | MATHEMATICAL LOGIC | UNIFIED GAUGE MODELS | QUANTUM FIELD THEORY | PARTICLE MODELS | SIMULATION 662100 -- General Theory of Particles & Fields-- (1992-)

Journal Article

Journal of High Energy Physics, ISSN 1126-6708, 11/2017, Volume 2017, Issue 11, pp. 1 - 38

In this note, we introduce and study a new class of “half integrands” in Cachazo-He-Yuan (CHY) formula, which naturally generalize the so-called Parke-Taylor...

Scattering Amplitudes | Superstrings and Heterotic Strings | Quantum Physics | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | AMPLITUDE | PHYSICS, PARTICLES & FIELDS | String theory | Polytopes | Feynman diagrams | Integrals | Physics - High Energy Physics - Theory | Nuclear and particle physics. Atomic energy. Radioactivity | High Energy Physics - Theory

Scattering Amplitudes | Superstrings and Heterotic Strings | Quantum Physics | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | AMPLITUDE | PHYSICS, PARTICLES & FIELDS | String theory | Polytopes | Feynman diagrams | Integrals | Physics - High Energy Physics - Theory | Nuclear and particle physics. Atomic energy. Radioactivity | High Energy Physics - Theory

Journal Article