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Feynman Integrals
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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 14 Pith papers
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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.
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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...
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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.
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Positive Integrands from Feynman Integrals in the Minkowski Regime
A method for converting Minkowski-regime Feynman parameter integrals into sums of real, positive integrands with complex prefactors, eliminating contour deformation and speeding up numerical evaluation.
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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.
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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.
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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.
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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.
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Analytic Regression of Feynman Integrals from High-Precision Numerical Sampling
Multi-point lattice reduction on high-precision numerical samples can recover exact analytic expressions for multi-loop Feynman integrals with rational coefficients.
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Soft Factorisation and Exponentiation from Schwinger-Space Geometry
Soft-hard factorization and exponentiation of infrared divergences in QED are derived from graph Laplacians and tropical rays in Schwinger parameter space.
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Current-current operator contribution to the decay matrix in $B$-meson mixing at next-to-next-to-leading order of QCD
The full charm-mass dependence of the three-loop current-current contribution to the B-meson decay matrix is computed, yielding Delta_Gamma_s = (0.077 +/- 0.016) ps^-1 with the leading-term perturbative error reduced ...
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Refining Integration-by-Parts Reduction of Feynman Integrals with Machine Learning
Machine learning program search rediscovers state-of-the-art integration-by-parts seeding heuristics and finds a modestly smaller seed set for a single two-loop benchmark integral.
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High-precision numerical evaluation of Lauricella functions
A Mathematica package computes high-precision epsilon-expansions of Lauricella functions using one-dimensional Frobenius series and interpolation.
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$\texttt{PrecisionLauricella}$: package for numerical computation of Lauricella functions depending on a parameter
PrecisionLauricella is a Mathematica package that computes epsilon-expansions of Lauricella F_A, F_B, and F_D functions for n up to 3 using Frobenius-series analytic continuation.
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