Yangian-invariant fishnet integrals in two dimensions as volumes of Calabi-Yau varieties
We argue that ℓ-loop Yangian-invariant fishnet integrals in two dimensions are connected to
a family of Calabi-Yau ℓ folds. The value of the integral can be computed from the periods of …
a family of Calabi-Yau ℓ folds. The value of the integral can be computed from the periods of …
From polygons and symbols to polylogarithmic functions
A bstract We present a review of the symbol map, a mathematical tool introduced by
Goncharov and used by him and collaborators in the context of\(\mathcal {N}\)= 4 SYM for …
Goncharov and used by him and collaborators in the context of\(\mathcal {N}\)= 4 SYM for …
Bounded collection of Feynman integral Calabi-Yau geometries
We define the rigidity of a Feynman integral to be the smallest dimension over which it is
nonpolylogarithmic. We prove that massless Feynman integrals in four dimensions have a …
nonpolylogarithmic. We prove that massless Feynman integrals in four dimensions have a …
[HTML][HTML] The elliptic dilogarithm for the sunset graph
S Bloch, P Vanhove - Journal of Number Theory, 2015 - Elsevier
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 two dimensions. We give …
evaluated the sunset integral for all identical internal masses in two dimensions. We give …
Constraints on sequential discontinuities from the geometry of on-shell spaces
A bstract We present several classes of constraints on the discontinuities of Feynman
integrals that go beyond the Steinmann relations. These constraints follow from a geometric …
integrals that go beyond the Steinmann relations. These constraints follow from a geometric …
[图书][B] Evaluating feynman integrals
VA Smirnov - 2004 - books.google.com
The problem of evaluating Feynman integrals over loop momenta has existed from the early
days of perturbative quantum field theory. Although a great variety of methods for evaluating …
days of perturbative quantum field theory. Although a great variety of methods for evaluating …
Massive Feynman diagrams and inverse binomial sums
AI Davydychev, MY Kalmykov - Nuclear Physics B, 2004 - Elsevier
When calculating higher terms of the ɛ-expansion of massive Feynman diagrams, one
needs to evaluate particular cases of multiple inverse binomial sums. These sums are …
needs to evaluate particular cases of multiple inverse binomial sums. These sums are …
[图书][B] Feynman integral calculus
VA Smirnov, VA Smirnov - 2006 - Springer
This is a textbook version of my previous book [190]. Problems and solutions have been
included, Appendix G has been added, more details have been presented, recent …
included, Appendix G has been added, more details have been presented, recent …
[PDF][PDF] Feynman amplitudes and cosmic Galois group
F Brown - arXiv preprint arXiv:1512.06409, 2015 - arxiv.org
arXiv:1512.06409v3 [math-ph] 1 Feb 2017 Page 1 arXiv:1512.06409v3 [math-ph] 1 Feb 2017
FEYNMAN AMPLITUDES, COACTION PRINCIPLE, AND COSMIC GALOIS GROUP FRANCIS …
FEYNMAN AMPLITUDES, COACTION PRINCIPLE, AND COSMIC GALOIS GROUP FRANCIS …
Three point energy correlators in the collinear limit: symmetries, dualities and analytic results
A bstract Energy Correlators measure the energy deposited in multiple detectors as a
function of the angles between the detectors. In this paper, we analytically compute the three …
function of the angles between the detectors. In this paper, we analytically compute the three …