More uses for Wilson loops: Perturbation theory without Feynman diagrams

1984 ◽  
Vol 29 (8) ◽  
pp. 1772-1783 ◽  
Author(s):  
William Celmaster ◽  
Eve Kovacs
Keyword(s):  
Perturbation Theory ◽  
Feynman Diagrams ◽  
Wilson Loops

scholarly journals Stochastic computation of g − 2 in QED

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Ryuichiro Kitano ◽  
Hiromasa Takaura ◽  
Shoji Hashimoto
Keyword(s):  
Perturbation Theory ◽  
Numerical Computation ◽  
Magnetic Moment ◽  
Anomalous Magnetic Moment ◽  
Stochastic Perturbation ◽  
Higher Order ◽  
Feynman Diagrams ◽  
Perturbative Series ◽  
Physical Quantities

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.

NULL ZIG-ZAG WILSON LOOPS IN $\mathcal{N}=4$ SYM

2010 ◽  
Vol 25 (08) ◽  
pp. 627-639
Author(s):  
ZHIFENG XIE
Keyword(s):  
Perturbation Theory ◽  
Wilson Loop ◽  
Wilson Loops ◽  
Finite Part ◽  
Expectation Value ◽  
Line Segments ◽  
Yang Mills ◽  
Circular Shape ◽  
The One ◽  
Arbitrary Shapes

In planar [Formula: see text] supersymmetric Yang–Mills theory we have studied one kind of (locally) BPS Wilson loops composed of a large number of light-like segments, i.e. null zig-zags. These contours oscillate around smooth underlying spacelike paths. At one-loop in perturbation theory, we have compared the finite part of the expectation value of null zig-zags to the finite part of the expectation value of non-scalar-coupled Wilson loops whose contours are the underlying smooth spacelike paths. In arXiv:0710.1060 [hep-th] it was argued that these quantities are equal for the case of a rectangular Wilson loop. Here we present a modest extension of this result to zig-zags of circular shape and zig-zags following non-parallel, disconnected line segments and show analytically that the one-loop finite part is indeed that given by the smooth spacelike Wilson loop without coupling to scalars which the zig-zag contour approximates. We make some comments regarding the generalization to arbitrary shapes.

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

2018 ◽  
Vol 173 ◽  
pp. 02001 ◽  
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.

scholarly journals GLUON SCATTERING AMPLITUDES FROM GAUGE/STRING DUALITY AND INTEGRABILITY

2013 ◽  
Vol 21 ◽  
pp. 1-21
Author(s):  
YUJI SATOH
Keyword(s):  
Perturbation Theory ◽  
Scattering Amplitudes ◽  
String Duality ◽  
Bethe Ansatz ◽  
Strong Coupling ◽  
Minimal Surfaces ◽  
Wilson Loops ◽  
Thermodynamic Bethe Ansatz ◽  
Yang Mills ◽  
Sine Gordon Model

We discuss gluon scattering amplitudes/null-polygonal Wilson loops of [Formula: see text] super Yang-Mills theory at strong coupling based on the gauge/string duality and its underlying integrability. We focus on the amplitudes/Wilson loops corresponding to the minimal surfaces in AdS3, which are described by the thermodynamic Bethe ansatz equations of the homogeneous sine-Gordon model. Using conformal perturbation theory and an interesting relation between the g-function (boundary entropy) and the T-function, we derive analytic expansions around the limit where the Wilson loops become regular-polygonal. We also compare our analytic results with those at two loops, to find that the rescaled remainder functions are close to each other for all multi-point amplitudes.

Quantum Field Theory

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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