Application of Deformed Lie Algebras to Non-Perturbative Quantum Field Theory

2017 ◽  
Vol 84 (1-2) ◽  
pp. 109
Author(s):  
Ali Shojaei-Fard
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Differential Geometry ◽  
Lie Algebras ◽  
Feynman Diagrams ◽  
Quantum Field ◽  
New Class ◽  
Noncommutative Differential Geometry ◽  
Perturbative Quantum ◽  
Perturbative Quantum Field Theory

The manuscript implements Connes-Kreimer Hopf algebraic renormalization of Feynman diagrams and Dubois-Violette type noncommutative differential geometry to discover a new class of differential calculi with respect to infinite formal expansions of Feynman diagrams which are generated by Dyson-Schwinger equations.

FIRST NON-VANISHING SELF-LINKING OF KNOTS (I) COMBINATORIC AND DIAGRAMMATIC STUDY

2011 ◽  
Vol 20 (12) ◽  
pp. 1637-1648 ◽  
Author(s):  
CHUN-CHUNG HSIEH
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Knot Theory ◽  
Feynman Diagrams ◽  
Quantum Field ◽  
Borromean Rings ◽  
Diagrammatic Representation ◽  
Perturbative Quantum ◽  
Perturbative Quantum Field Theory ◽  
Chern Simons

In this paper, following the scheme of [Borromean rings and linkings, J. Geom. Phys.60 (2010) 823–831; Combinatoric and diagrammatic study in knot theory, J. Knot Theory Ramifications16 (2007) 1235–1253; Massey–Milnor linking = Chern–Simons–Witten graphs, J. Knot Theory Ramifications17 (2008) 877–903], we study the first non-vanishing self-linkings of knots, aiming at the study of combinatorial formulae and diagrammatic representation. The upshot of perturbative quantum field theory is to compute the Feynman diagrams explicitly, though it is impossible in general. Along this line in this paper we could not only compute some Feynman diagrams, but also give the explicit and combinatorial formulae.

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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