REVIEW 24 cited by
Feynman Integrals
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
Feynman Integrals
read the original abstract
This course on Feynman integrals starts from the basics, requiring only knowledge from special relativity and undergraduate mathematics. Topics from quantum field theory and advanced mathematics are introduced as they are needed. The course covers modern developments in the field of Feynman integrals. Topics included in this course are: Representations of Feynman integrals, integration-by-parts, differential equations, intersection theory, multiple polylogarithms, Gelfand-Kapranov-Zelevinsky systems, coactions and symbols, cluster algebras, elliptic Feynman integrals, motives associated to Feynman integrals.
Forward citations
Cited by 24 Pith papers
-
The multiloop sunset to all orders
Multiloop sunset integrals in D=2 are expressed as convergent sums of symmetric polynomials in logarithms of mass ratios, with a dimension-raising operator that propagates the result to D=4-2ε.
-
On Cosmological Correlators at One Loop
The one-loop triangle in-in correlator of massless scalars in flat space is evaluated in closed form in terms of dilogarithms, with Landau analysis revealing its physical singularities and a partial-energy factorisati...
-
Degenerations of flat connections on Riemann surfaces
Enriquez and DHS kernels on genus-h surfaces close under non-separating degeneration to genus h-1 kernels with two punctures whose generators are Bernoulli series in the original Lie algebra elements.
-
Resonance and Differential Reduction of Feynman Integrals
The paper develops reduction operators from resonance in GKZ systems to contract edges in Feynman graphs for one-loop, sunrise, and banana graphs, closing differential equation systems to master integrals.
-
The gravitational Compton amplitude at third post-Minkowskian order
Gravitational Compton amplitude computed to third post-Minkowskian order via worldline EFT with infrared and forward divergences regulated to connect to black hole perturbation theory.
-
Analytic result of a three-loop integral family in the Higgs decay to four massive bottom quarks
Analytic master-integral results through O(ε²) are obtained for a three-loop family containing elliptic and K3 geometries by building and solving a mixed-sector ε-factorized differential equation.
-
Towards Equations for String Amplitudes
Tree-level open bosonic string amplitudes satisfy a complete system of linear difference equations in kinematic variables whose number matches the independent parameters, recovering algebraic QFT structure as alpha ap...
-
Picard-Fuchs Equations of Twisted Differential forms associated to Feynman Integrals
An extension of the Griffiths-Dwork algorithm produces twisted Picard-Fuchs operators for hypergeometric, elliptic, and Calabi-Yau motives from families of Feynman integrals.
-
Global Convergence of the Return Dynamics in the Class $\mathcal{O}_C$
Return dynamics in the class O_C converge globally to critical points of the thickness function by approximating adaptive gradient descent.
-
Curve integral formula for the M\"obius strip
A global Schwinger integral is constructed for Möbius-strip amplitudes and verified against the tropical limit of the type-I superstring Möbius amplitude.
-
New algorithms for Feynman integral reduction and $\varepsilon$-factorised differential equations
A geometric order relation in IBP reduction yields a master-integral basis with Laurent-polynomial differential equations on the maximal cut that are then ε-factorized.
-
Tensor Reduction of Sunset by Generating Function
A complete set of recurrence relations is derived to reduce any tensor integral of the sunset diagram to seven master integrals, using generating functions supplemented by syzygy equations.
-
Worldline effective field theory of inspiralling black hole binaries in presence of dark photon and axionic dark matter
Computes 1PN conservative dynamics for gravitational/EM/Proca fields and 2PN for scalar, plus radiation effects from axion-photon coupling at high PN orders in binary black hole systems with dark matter.
-
Soft Contributions Stabilize NNLO QCD Corrections to Quarkonium Production and Decay
Soft contributions stabilize NNLO QCD corrections for S-wave color-singlet quarkonium processes, yielding better perturbative convergence and experimental agreement.
-
Finite Massless Pentaboxes
Characterizes numerators yielding finite or evanescent massless pentabox integrals, gives compact generators via momentum basis and Gram determinants, and evaluates lowest-rank cases in polylogarithms and pentagon functions.
-
Genus drop involving non-hyperelliptic curves in Feynman integrals
The extra-involution mechanism for genus drop is a special case of unramified double covering between curves, which explains genus drops with non-hyperelliptic to hyperelliptic transitions in certain three-loop Feynma...
-
Global Convergence of the Return Dynamics in the Class $\mathcal{O}_C$
Return dynamics on class O_C domains with fixed convex core converge globally like adaptive gradient descent of the thickness function, with fixed points equal to thickness critical points.
-
Minkowski Space holography and Radon transform
Relates free scalar in Minkowski space to codimension-two sphere field via Radon transform to dS/EAdS slice and bulk reconstruction, with Mellin modes as generalized hypergeometric functions via Lee-Pomeransky method.
-
HyperFORM -- a FORM package for parametric integration with hyperlogarithms
A new open FORM package implements parametric hyperlogarithm integration, demonstrated on zigzag Feynman integrals up to six loops.
-
Unitarity Cuts, t-channel Divergences and the KLN Theorem for Unstable Particles
Authors formulate prescriptions for KLN cancellations of t-channel divergences in an unstable-particle model, showing scheme-independent results and steps toward finite inclusive observables.
-
Numerical analytical continuation of multivariate hypergeometric functions
A general numerical framework is described for high-precision evaluation and analytic continuation of multivariate hypergeometric functions via Pfaffian systems and the Frobenius method.
-
Comments on Celestial CFT and $AdS_{3}$ String Theory
Extends H3+-WZNW celestial CFT to holographically generate MHV amplitudes in Klein space, deriving dictionary, stress tensor, correlators, OPE and PDEs from KZ equations.
-
An Alternative Viewpoint on Kinematic Flow from Tubing Splitting
Reversing the direction of tubing evolution yields splitting rules that reproduce the kinematic flow differential equations at tree level and suggest time emerges from kinematic space in conformally coupled scalar mod...
-
Les Houches 2023 -- Physics at TeV Colliders: Report on the Standard Model Precision Wishlist
The report reviews progress since 2021 in fixed-order computations for LHC applications and identifies processes requiring missing higher-order corrections to match anticipated experimental precision.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.