scholarly journals Feynman Graphs, and Nerve Theorem for Compact Symmetric Multicategories (Extended Abstract)

2011 ◽  
Vol 270 (2) ◽  
pp. 105-113 ◽  
Author(s):  
André Joyal ◽  
Joachim Kock
Keyword(s):  
Feynman Graphs ◽  
Nerve Theorem

scholarly journals An algorithm to compute Born scattering amplitudes without Feynman graphs

1995 ◽  
Vol 358 (3-4) ◽  
pp. 332-338 ◽  
Author(s):  
Francesco Caravaglios ◽  
Mauro Moretti
Keyword(s):  
Scattering Amplitudes ◽  
Feynman Graphs

Second-type singularities of Feynman graphs

1964 ◽  
Vol 56 ◽  
pp. 161-173 ◽  
Author(s):  
V.E. Asribekov
Keyword(s):  
Feynman Graphs

Algebraic combinatorics and QFT

2021 ◽  
pp. 76-94
Author(s):  
Adrian Tanasa
Keyword(s):  
Hopf Algebra ◽  
Hochschild Cohomology ◽  
Algebraic Combinatorics ◽  
Fourth Section ◽  
Analytic Combinatorics ◽  
Multi Scale ◽  
Starting Point ◽  
Feynman Graphs ◽  
Perturbative Renormalization

We have seen in the previous chapter some of the non-trivial interplay between analytic combinatorics and QFT. In this chapter, we illustrate how yet another branch of combinatorics, algebraic combinatorics, interferes with QFT. In this chapter, after a brief algebraic reminder in the first section, we introduce in the second section the Connes–Kreimer Hopf algebra of Feynman graphs and we show its relation with the combinatorics of QFT perturbative renormalization. We then study the algebra's Hochschild cohomology in relation with the combinatorial Dyson–Schwinger equation in QFT. In the fourth section we present a Hopf algebraic description of the so-called multi-scale renormalization (the multi-scale approach to the perturbative renormalization being the starting point for the constructive renormalization programme).

From random matrices to random tensors

2021 ◽  
pp. 166-177
Author(s):  
Adrian Tanasa
Keyword(s):  
Matrix Models ◽  
Random Matrices ◽  
Mathematical Physics ◽  
Natural Generalization ◽  
Random Surface ◽  
The Third ◽  
Planar Surfaces ◽  
Tensor Models ◽  
Feynman Graphs ◽  
The Matrix

After a brief presentation of random matrices as a random surface QFT approach to 2D quantum gravity, we focus on two crucial mathematical physics results: the implementation of the large N limit (N being here the size of the matrix) and of the double-scaling mechanism for matrix models. It is worth emphasizing that, in the large N limit, it is the planar surfaces which dominate. In the third section of the chapter we introduce tensor models, seen as a natural generalization, in dimension higher than two, of matrix models. The last section of the chapter presents a potential generalisation of the Bollobás–Riordan polynomial for tensor graphs (which are the Feynman graphs of the perturbative expansion of QFT tensor models).

Triangulating Topological Spaces

1997 ◽  
Vol 07 (04) ◽  
pp. 365-378 ◽  
Author(s):  
Herbert Edelsbrunner ◽  
Nimish R. Shah
Keyword(s):  
Homotopy Equivalent ◽  
Topological Spaces ◽  
Sufficient Condition ◽  
Voronoi Cells ◽  
Delaunay Complex ◽  
Common Intersection ◽  
Finite Set ◽  
The Common ◽  
Nerve Theorem

Given a subspace [Formula: see text] and a finite set S⊆ℝd, we introduce the Delaunay complex, [Formula: see text], restricted by [Formula: see text]. Its simplices are spanned by subsets T⊆S for which the common intersection of Voronoi cells meets [Formula: see text] in a non-empty set. By the nerve theorem, [Formula: see text] and [Formula: see text] are homotopy equivalent if all such sets are contractible. This paper proves a sufficient condition for [Formula: see text] and [Formula: see text] be homeomorphic.

Feynman Graphs

2017 ◽  
pp. 159-176
Author(s):  
Andrei Smilga
Keyword(s):  
Feynman Graphs

ON THE INSERTION-ELIMINATION LIE ALGEBRA OF FEYNMAN GRAPHS

2004 ◽  
Author(s):  
KURUSCH EBRAHIMI-FARD ◽  
DIRK KREIMER ◽  
IGOR MENCATTINI
Keyword(s):  
Lie Algebra ◽  
Feynman Graphs
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