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Hopf Algebras, Renormalization and Noncommutative Geometry
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Hopf Algebras, Renormalization and Noncommutative Geometry
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We explore the relation between the Hopf algebra associated to the renormalization of QFT and the Hopf algebra associated to the NCG computations of transverse index theory for foliations.
Forward citations
Cited by 5 Pith papers
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Piecewise Symmetric Tensors
Every k-tensor is the unique sum of an m-piecewise-symmetric tensor and a (k-m)-piecewise-alternating tensor; the latter space is the annihilator of level-k signatures of m-segment paths.
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Tropicalized quantum field theory and global tropical sampling
Tropicalized massive scalar QFT is exactly solvable via a non-linear recursion for effective action coefficients that computes graph moduli space volumes, enabling a polynomial-time sampling algorithm for high-order p...
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On quantum $G$-structures
A quantum G-structure, defined as a reduction of a quantum frame resolution, itself forms a quantum frame resolution under a covariant first-order differential calculus.
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de Sitter Wavefunction from Quadrangular Polylogarithms: Chain Graphs
The n-site chain graph contribution to the de Sitter cosmological wavefunction in conformally coupled φ³ theory is expressed explicitly in terms of Rudenko's quadrangular polylogarithms.
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Homomorphism, substructure, and ideal: Elementary but rigorous aspects of renormalization group or hierarchical structure of topological orders
An algebraic RG formalism for topological orders uses ideals in fusion rings to encode noninvertible symmetries and condensation rules between anyons.
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