scholarly journals FEYNMAN DIAGRAMS VIA GRAPHICAL CALCULUS

2002 ◽  
Vol 11 (07) ◽  
pp. 1095-1131 ◽  
Author(s):  
DOMENICO FIORENZA ◽  
RICCARDO MURRI
Keyword(s):  
Quantum Gravity ◽  
Asymptotic Expansions ◽  
Feynman Diagrams ◽  
Ribbon Graphs ◽  
Graphical Calculus

We use Reshetikhin-Turaev graphical calculus to define Feynman diagrams and prove that asymptotic expansions of Gaussian integrals can be written as a sum over a suitable family of graphs. We discuss how different kinds of interactions give rise to different families of graphs. In particular, we show how symmetric and cyclic interactions lead to "ordinary" and "ribbon" graphs respectively. As an example, the 't Hooft-Kontsevich model for 2D quantum gravity is treated in some detail.

scholarly journals Feynman diagrams, ribbon graphs, and topological recursion of Eynard-Orantin

2018 ◽  
Vol 2018 (6) ◽  
Author(s):  
K. Gopalakrishna ◽  
Patrick Labelle ◽  
Vasilisa Shramchenko
Keyword(s):  
Feynman Diagrams ◽  
Ribbon Graphs ◽  
Topological Recursion

scholarly journals Hidden quantum gravity in 4D Feynman diagrams: emergence of spin foams

2007 ◽  
Vol 24 (8) ◽  
pp. 2027-2060 ◽  
Author(s):  
Aristide Baratin ◽  
Laurent Freidel
Keyword(s):  
Quantum Gravity ◽  
Feynman Diagrams

scholarly journals ASYMPTOTIC EXPANSIONS IN MOMENTA AND MASSES AND CALCULATION OF FEYNMAN DIAGRAMS

1995 ◽  
Vol 10 (21) ◽  
pp. 1485-1499 ◽  
Author(s):  
V.A. SMIRNOV
Keyword(s):  
Asymptotic Expansions ◽  
Feynman Diagrams

General results on asymptotic expansions of Feynman diagrams in momenta and/or masses are reviewed. It is shown how they are applied for calculation of massive diagrams.

scholarly journals Hidden quantum gravity in 3D Feynman diagrams

2007 ◽  
Vol 24 (8) ◽  
pp. 1993-2026 ◽  
Author(s):  
Aristide Baratin ◽  
Laurent Freidel
Keyword(s):  
Quantum Gravity ◽  
Feynman Diagrams

scholarly journals The two-sphere partition function in two-dimensional quantum gravity at fixed area

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Beatrix Mühlmann
Keyword(s):  
Partition Function ◽  
Quantum Gravity ◽  
Path Integral ◽  
Central Charge ◽  
Gravity Theory ◽  
Feynman Diagrams ◽  
Two Dimensional ◽  
Loop Order ◽  
Fixed Area

Abstract We discuss two-dimensional quantum gravity coupled to conformal matter and fixed area in a semiclassical large and negative matter central charge limit. In this setup the gravity theory — otherwise highly fluctuating — admits a round two-sphere saddle. We discuss the two-sphere partition function up to two-loop order from the path integral perspective. This amounts to studying Feynman diagrams incorporating the fixed area constraint on the round two-sphere. In particular we find that all ultraviolet divergences cancel to this order. We compare our results with the two-sphere partition function obtained from the DOZZ formula.

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