Computer generation of Feynman diagrams for perturbation theory I. General algorithm

Abstract We perform a numerical computation of the anomalous magnetic moment (g − 2) of the electron in QED by using the stochastic perturbation theory. Formulating QED on the lattice, we develop a method to calculate the coefficients of the perturbative series of g − 2 without the use of the Feynman diagrams. We demonstrate the feasibility of the method by performing a computation up to the α3 order and compare with the known results. This program provides us with a totally independent check of the results obtained by the Feynman diagrams and will be useful for the estimations of not-yet-calculated higher order values. This work provides an example of the application of the numerical stochastic perturbation theory to physical quantities, for which the external states have to be taken on-shell.

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Directed Percolation: Calculation of Feynman Diagrams in the Three-Loop Approximation

EPJ Web of Conferences ◽

10.1051/epjconf/201817302001 ◽

2018 ◽

Vol 173 ◽

pp. 02001 ◽

Cited By ~ 3

Author(s):

Loran Ts. Adzhemyan ◽

Michal Hnatič ◽

Mikhail V. Kompaniets ◽

Tomáš Lučivjanský ◽

Lukáš Mižišin

Keyword(s):

Perturbation Theory ◽

Statistical Physics ◽

Numerical Technique ◽

Feynman Diagrams ◽

Directed Percolation ◽

Loop Order ◽

Percolation Process ◽

Anomalous Dimensions ◽

Loop Approximation ◽

Universal Properties

The directed bond percolation process is an important model in statistical physics. By now its universal properties are known only up to the second-order of the perturbation theory. Here, our aim is to put forward a numerical technique with anomalous dimensions of directed percolation to higher orders of perturbation theory and is focused on the most complicated Feynman diagrams with problems in calculation. The anomalous dimensions are computed up to three-loop order in ε = 4 − d.

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Erratum: Calculation of Feynman diagrams in superstring perturbation theory

Physical Review D ◽

10.1103/physrevd.52.6201.2 ◽

1995 ◽

Vol 52 (10) ◽

pp. 6201-6202 ◽

Cited By ~ 2

Author(s):

G. S. Danilov

Keyword(s):

Perturbation Theory ◽

Feynman Diagrams

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More uses for Wilson loops: Perturbation theory without Feynman diagrams

Physical Review D ◽

10.1103/physrevd.29.1772 ◽

1984 ◽

Vol 29 (8) ◽

pp. 1772-1783 ◽

Cited By ~ 3

Author(s):

William Celmaster ◽

Eve Kovacs

Keyword(s):

Perturbation Theory ◽

Feynman Diagrams ◽

Wilson Loops

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Quantum Field Theory

Statistical Field Theory ◽

10.1093/oso/9780198788102.003.0007 ◽

2020 ◽

pp. 237-288

Author(s):

Giuseppe Mussardo

Keyword(s):

Field Theory ◽

Quantum Field Theory ◽

Perturbation Theory ◽

Canonical Quantization ◽

Feynman Diagrams ◽

Field Theories ◽

Coordinate Space ◽

Matrix Formalism ◽

Quantum Field ◽

Transfer Matrix Formalism

Chapter 7 covers the main reasons for adopting the methods of quantum field theory (QFT) to study the critical phenomena. It presents both the canonical quantization and the path integral formulation of the field theories as well as the analysis of the perturbation theory. The chapter also covers transfer matrix formalism and the Euclidean aspects of QFT, the field theory of the Ising model, Feynman diagrams, correlation functions in coordinate space, the Minkowski space and the Legendre transformation and vertex functions. Everything in this chapter will be needed sooner or later, since it highlights most of the relevant aspects of quantum field theory.

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Finite calculation of divergent self-energy diagrams

Canadian Journal of Physics ◽

10.1139/p03-103 ◽

2003 ◽

Vol 81 (12) ◽

pp. 1433-1445 ◽

Cited By ~ 6

Author(s):

A Aste ◽

D Trautmann

Keyword(s):

Perturbation Theory ◽

Dispersion Relation ◽

Imaginary Part ◽

Feynman Diagram ◽

Feynman Diagrams ◽

Energy Diagram ◽

The Real ◽

Self Energy ◽

Single Integral ◽

Analytic Expression

Using dispersive techniques, it is possible to avoid ultraviolet divergences in the calculation of Feynman diagrams, making subsequent regularization of divergent diagrams unnecessary. We give a simple introduction to the most important features of such dispersive techniques in the framework of the so-called finite causal perturbation theory. The method is also applied to the "divergent" general massive two-loop sunrise self-energy diagram, where it leads directly to an analytic expression for the imaginary part of the diagram in accordance with the literature, whereas the real part can be obtained by a single integral dispersion relation. It is pointed out that dispersive methods have been known for decades and have been applied to several nontrivial Feynman diagram calculations.PACS Nos.: 11.10.z, 11.15.Bt, 12.20.Ds, 12.38.Bx

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