Hopf Algebras, Renormalization and Noncommutative Geometry

Abstract

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.

49 pages, Latex, 14 Fig's using epsf

References in corpus (2)

• Hopf algebras, cyclic cohomology and the transverse index theory
• On Overlapping Divergences

Cited by in corpus (320)

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• Nested Sums, Expansion of Transcendental Functions and Multi-Scale Multi-Loop Integrals
• Muon g-2: Review of Theory and Experiment
• A Short Survey of Noncommutative Geometry
• Analytic and Algorithmic Aspects of Generalized Harmonic Sums and Polylogarithms
• Exact solutions of Dyson-Schwinger equations for iterated one-loop integrals and propagator-coupling duality
• Nonabelian generalized Lax pairs, the classical Yang-Baxter equation and PostLie algebras
• A Unified Algebraic Approach to Classical Yang-Baxter Equation
• A Lie theoretic approach to renormalization
• Combinatorial Hopf algebras in quantum field theory I
• Two interacting Hopf algebras of trees
• On Overlapping Divergences
• Supercharacters, symmetric functions in noncommuting variables, and related Hopf algebras
• Integrable Renormalization II: the general case
• Left-symmetric Bialgebras and An Analogue of the Classical Yang-Baxter Equation
• Quantum Groups and Noncommutative Geometry
• On post-Lie algebras, Lie--Butcher series and moving frames
• Diagrammatic Hopf algebra of cut Feynman integrals: the one-loop case
• Hopf algebras in renormalization theory: Locality and Dyson-Schwinger equations from Hochschild cohomology
• Anatomy of a gauge theory
• The algebraic structure of cut Feynman integrals and the diagrammatic coaction
• Pre-Lie algebras and the rooted trees operad
• Spitzer's Identity and the Algebraic Birkhoff Decomposition in pQFT
• A noncommutative Bohnenblust-Spitzer identity for Rota-Baxter algebras solves Bogoliubov's recursion
• Ward identities and combinatorics of rainbow tensor models
• Free Rota-Baxter algebras and rooted trees
• Recursive relations in the core Hopf algebra
• Insertion and Elimination: the doubly infinite Lie algebra of Feynman graphs
• Universal Racah matrices and adjoint knot polynomials. I. Arborescent knots
• Decomposition spaces, incidence algebras and Möbius inversion I: basic theory
• Combinatorics of Rooted Trees and Hopf Algebras
• Hopf algebra approach to Feynman diagram calculations
• From Physics to Number Theory via Noncommutative Geometry, Part II: Renormalization, the Riemann-Hilbert correspondence, and motivic Galois theory
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• Combinatoric explosion of renormalization tamed by Hopf algebra: 30-loop Pade-Borel resummation
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• Rainbow tensor model with enhanced symmetry and extreme melonic dominance
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• Shuffle relations for regularised integrals of symbols
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• Renormalization of the noncommutative phi^3 model through the Kontsevich model
• Resonance based schemes for dispersive equations via decorated trees
• The Jacobian Conjecture as a Problem of Perturbative Quantum Field Theory
• Birkhoff type decompositions and the Baker-Campbell-Hausdorff recursion
• Combinatorics of (perturbative) quantum field theory
• Feynman Polytopes and the Tropical Geometry of UV and IR Divergences
• Casimir effect between ponderable media as modeled by the standard model extension
• Dyson Schwinger Equations: From Hopf algebras to Number Theory
• Algebraic structures in quantum gravity
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• Analytic Computing Methods for Precision Calculations in Quantum Field Theory
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• Cut and join operator ring in Aristotelian tensor model
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• A construction of the rough path above fractional Brownian motion using Volterra's representation
• Exponential Renormalization II: Bogoliubov's R-operation and momentum subtraction schemes
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• On Classification of Finite-Dimensional Superbialgebras and Hopf Superalgebras
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• Hopf Algebras in General and in Combinatorial Physics: a practical introduction
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• A combinatorial Hopf algebra for nonlinear output feedback control systems
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• Planarly branched rough paths and rough differential equations on homogeneous spaces
• Renormalization and computation I: motivation and background
• Classification of Graded Left-symmetric Algebra Structures on Witt and Virasoro Algebras
• Renormalization and Mellin transforms
• Growth estimates for Dyson-Schwinger equations
• Algebraic renormalisation of regularity structures
• Rota-Baxter operators on $sl(2,C)$ and solutions of the classical Yang-Baxter equation
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• Bijective 1-cocycles and classification of 3-dimensional Left-symmetric Algebras
• The core Hopf algebra
• On the trees of quantum fields
• Groupoids and Faa di Bruno formulae for Green functions in bialgebras of trees
• New mathematical structures in renormalizable quantum field theories
• The geometry of the space of branched Rough Paths
• Hom Gel'fand-Dorfman bialgebras and Hom-Lie conformal algebras
• Hölder-continuous rough paths by Fourier normal ordering
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• Connes-Kreimer-Epstein-Glaser Renormalization
• Algebraic deformation for (S)PDEs
• Noncommutative renormalization for massless QED
• Determinations of rational Dedekind-zeta invariants of hyperbolic manifolds and Feynman knots and links
• Algebraic Birkhoff Factorization and the Euler-Maclaurin Formula on Cones
• The SAGEX Review on Scattering Amplitudes, Chapter 4: Multi-loop Feynman Integrals
• BiHom-pre-Lie algebras, BiHom-Leibniz algebras and Rota-Baxter operators on BiHom-Lie algebras
• Some remarks on q-deformed multiple polylogarithms
• Coupling of spacetime atoms and spin foam renormalisation from group field theory
• Harmonic sums and polylogarithms at non-positive multi-indices
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• Matrix Representation of Renormalization in Perturbative Quantum Field Theory
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• Algebraic Birkhoff decomposition and its applications
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• Stochastic expansions and Hopf algebras
• A Noncommutative Symmetric System over the Grossman-Larson Hopf Algebra of Labeled Rooted Trees
• Where do the tedious products of zetas come from?
• Algebraic structures associated to operads
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• Renormalization, Hopf algebras and Mellin transforms
• Commutative Hopf algebras of permutations and trees
• Quasi-shuffle algebras and renormalisation of rough differential equations
• On the Invariance of Residues of Feynman Graphs
• Multivariate Stirling Polynomials of the first and second kind
• Pluriassociative algebras II: The polydendriform operad and related operads
• Rota-Baxter multiplicative 3-ary Hom-Nambu-Lie algebras
• Decay Rate of Iterated Integrals of Branched Rough Paths
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• On an extension of Knuth's rotation correspondence to reduced planar trees
• Loops on surfaces, Feynman diagrams, and trees
• The uses of Connes and Kreimer's algebraic formulation of renormalization theory
• Unique factorization in perturbative QFT
• On the antipode of Kreimer's Hopf algebra
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• Higher loop renormalization of a supersymmetric field theory
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• Feynman diagrams and polylogarithms: shuffles and pentagons
• The combinatorics of Green's functions in planar field theories
• Infinitesimal unitary Hopf algebras and planar rooted forests
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• On the Connes-Moscovici Hopf algebra associated to the diffeomorphisms of a manifold
• Faà di Bruno for operads and internal algebras
• Invariant Differential Forms on Complexes of Graphs and Feynman Integrals
• New splittings of operations of Poisson algebras and transposed Poisson algebras and related algebraic structures
• Relating the Connes-Kreimer and Grossman-Larson Hopf algebras built on rooted trees
• On the structure of cofree Hopf algebras
• Doubling bialgebras of finite topologies
• Quasi-geometric rough paths and rough change of variable formula
• Eulerian idempotent, pre-Lie logarithm and combinatorics of trees
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• Left-symmetric Superalgebra Structures on the Super-Virasoro Algebras
• A Survey on the Munthe-Kaas-Wright Hopf Algebra
• A class of Lie conformal superalgebras in higher dimensions
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• Free Rota-Baxter family algebras and Free (tri)dendriform family algebras
• Overview of (pro-)Lie group structures on Hopf algebra character groups
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• Double shuffle relations and renormalization of multiple zeta values
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• The algebraic and geometric classification of nilpotent left-symmetric algebras
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• Free Rota-Baxter systems and a Hopf algebra structure
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• Categorification of Hopf algebras of rooted trees
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• Rota-Baxter Operators on pre-Lie superalgebras and beyond
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• QED Hopf algebras on planar binary trees
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• Hopf algebras on planar trees and permutations
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• Sequences of Trees and Higher-Order Renormalization Group Equations
• Rota's program on algebraic operators, rewriting systems and Gröbner-Shirshov bases
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• On the Hopf Algebraic Structure of Lie Group Integrators
• Coalescent tree based functional representations for some Feynman-Kac particle models
• Connes-Kreimer quantizations and PBW theorems for pre-Lie algebras
• Gröbner-Shirshov bases for Rota-Baxter algebras
• On Hopf algebra structures over free operads
• Sur une série en arbres à deux paramètres
• Hopf algebras in noncommutative geometry
• Algèbres de greffes
• Card-Shuffling via Convolutions of Projections on Combinatorial Hopf Algebras
• Pathlike Co/Bialgebras and their Antipodes with Applications to Bi- and Hopf Algebras Appearing in Topology, Number Theory and Physics
• Filtrations in Dyson-Schwinger equations: next-to^{j} -leading log expansions systematically
• A renormalized rough path over fractional Brownian motion
• The geometry of controlled rough paths
• Multi-indices coproducts from ODEs to singular SPDEs
• The necklace Lie coalgebra and renormalization algebras
• Classification of differentials and Cartan calculus on bicrossproducts
• More Series related to the Euler Series
• Hopf algebras and Dyson-Schwinger equations
• Examples of Com-PreLie Hopf algebras
• Mulitgraded Dyson-Schwinger systems
• Algebra for quantum fields
• Cocommutative Hopf algebras of permutations and trees
• The Hopf Algebra of Renormalization, Normal Coordinates and Kontsevich Deformation Quantization
• Generalized prelie and permutative algebras
• New parameters of Non-commutativity in Quantum Mechanics
• Generalized Matsumoto-Tits sections and quantum quasi-shuffle algebras
• Subdivergence-free gluings of trees
• A remainder estimate for branched rough differential equations
• On the definition of a solution to a rough differential equation
• Cofree Com-PreLie algebras
• Translations of rough paths in combinatorial Hopf algebras
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• Leading log expansion of combinatorial Dyson Schwinger equations
• Branched Itô formula and natural Itô-Stratonovich isomorphism
• On PreLie algebras with divided symmetries
• Pluriassociative and polydendriform algebras
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• Ecalle's averages, Rota-Baxter algebras and the construction of moulds
• Weighted rooted trees and deformations of operads
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• An antipode formula for the natural Hopf algebra of a set operad
• Operated semigroups, Motzkin paths and rooted trees
• Combinatorial Algebra for second-quantized Quantum Theory
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• Rooted trees for 3d Navier-Stokes equation
• Automorphisms of the Cuntz algebras
• Structure of the Loday-Ronco Hopf algebra of trees
• A rough path over multidimensional fractional Brownian motion with arbitrary Hurst index by Fourier normal ordering
• A sharp analysis of the mixing time for random walk on rooted trees
• Coalgebras of words and phrases
• Noncommutative geometry of foliations
• Universal Hopf Algebra of Renormalization and Hopf Algebras of Rooted Trees
• Lectures on Noncommutative Geometry
• On a noncommutative deformation of the Connes-Kreimer algebra
• The interface of noncommutative geometry and physics
• Symetries Galoisiennes et Renormalisation
• Free hyperplane arrangements associated to labeled rooted trees
• Introduction to Hopf algebras in renormalization and noncommutative geometry
• Bogoliubov type recursions for renormalisation in regularity structures
• Classification of orbit closures in the variety of 3-dimensional Novikov algebras
• Hopf algebra and renormalization: A brief review
• Classification of monomial Rota-Baxter operators on k[x]
• Hopf algebras: motivations and examples
• Left ideals in an enveloping algebra, prelie products and applications to simple complex Lie algebras
• Rota-Baxter Hom-Lie-admissible algebras
• Dihedral symmetries of multiple logarithms
• Limbs and Cospectral Vertices in Trees
• Hopf Algebra Primitives in Perturbation Quantum Field Theory
• Noncommutative geometry and quantization
• Rooted trees, Feynman graphs, and Hecke correspondences
• Quadratic Leibniz conformal algebras
• Can we make sense out of "Tensor Field Theory"?
• Integrability and Matrix Models
• Doubling pre-Lie algebra of rooted trees
• Ecalle's paralogarithmic resurgence monomials and effective synthesis
• Localization of Rota-Baxter algebras
• The smooth algebra of a one-dimensional singular foliation
• Tropicalized quantum field theory and global tropical sampling
• An Overview of Hopf Algebras of Trees and Their Actions on Functions
• Bialgebra of specified graphs and external structures
• {sigma, tau}-Rota-Baxter operators, infinitesimal Hom-bialgebras and the associative (Bi)Hom-Yang-Baxter equation
• Hopf algebroids and secondary characteristic classes
• Renormalization group-like proof of the universality of the Tutte polynomial for matroids
• Some infinite series related to Feynman diagrams
• Dynkin operators and renormalization group actions in pQFT
• Finite dimensional comodules over the Hopf algebra of rooted trees
• Flows driven by multi-indices Rough Paths
• On the sub-adjacent Hopf algebra of the universal enveloping algebra of a post-Lie algebra
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• Simply Generated Trees, B-series and Wigner Processes
• A mathematical perspective on the phenomenology of non-perturbative Quantum Field Theory
• Nonlinear Perturbation Theory
• Mode d'emploi de la théorie constructive des champs bosoniques (A user's guide to bosonic constructive field theory)
• Simple physical applications of a groupoid structure
• Bidendriform bialgebras, trees, and free quasi-symmetric functions
• Characteristics of Rota-Baxter Algebras
• Noncommutative Symmetric Systems over Associative Algebras
• Riemann-Hilbert Problem and Quantum Field Theory: Integrable Renormalization, Dyson-Schwinger Equations
• A Generalization of Connes-Kreimer Hopf Algebra
• Combinatorial Route to Algebra: The Art of Composition & Decomposition
• Commutative combinatorial Hopf algebras
• On the Hopf Algebra of Rooted Trees
• The signed permutation group on Feynman graphs
• Combinatorial Dyson-Schwinger equations and inductive data types
• Coherent unit actions on braided operads and Hopf algebras
• The bigraft algebras