SECTOR DECOMPOSITION

2008 ◽  
Vol 23 (10) ◽  
pp. 1457-1486 ◽  
Author(s):  
GUDRUN HEINRICH
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Phase Space ◽  
General Algorithm ◽  
Constructive Method ◽  
Quantum Field ◽  
Matrix Elements ◽  
Feynman Parameter ◽  
Perturbative Quantum ◽  
Perturbative Quantum Field Theory

Sector decomposition is a constructive method to isolate divergences from parameter integrals occurring in perturbative quantum field theory. We explain the general algorithm in detail and review its application to multiloop Feynman parameter integrals as well as infrared divergent phase-space integrals over real radiation matrix elements.

Renormalization of quantum field theory on Riemannian manifolds

2019 ◽  
Vol 31 (06) ◽  
pp. 1950017
Author(s):  
Nguyen Viet Dang ◽  
Estanislao Herscovich
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Riemannian Manifolds ◽  
Quantum Field ◽  
Local Method ◽  
Open Set ◽  
Perturbative Quantum ◽  
Perturbative Quantum Field Theory

In this paper, we provide a simple pedagogical proof of the existence of covariant renormalizations in Euclidean perturbative quantum field theory on closed Riemannian manifolds, following the Epstein–Glaser philosophy. We rely on a local method that allows us to extend a distribution defined on an open set [Formula: see text] to the whole manifold [Formula: see text].

MASSEY–MILNOR LINKING = CHERN–SIMONS–WITTEN GRAPHS

2008 ◽  
Vol 17 (07) ◽  
pp. 877-903 ◽  
Author(s):  
CHUN-CHUNG HSIEH
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Configuration Space ◽  
Quantum Field ◽  
Perturbative Quantum ◽  
Perturbative Quantum Field Theory ◽  
Chern Simons ◽  
Configuration Space Integrals

We express the first non-vanishing Massey–Milnor linkings in terms of Chern–Simons–Witten configuration space integrals in perturbative quantum field theory.

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