Algorithmic derivation of Dyson-Schwinger equations
TL;DR: The Mathematica package DoDSE 1 is introduced which derives the Dyson–Schwinger equations graphically once the interactions of the theory are specified and is suitable for an implementation within a symbolic programming language.
About: This article is published in Computer Physics Communications.The article was published on 2009-06-01 and is currently open access. It has received 58 citations till now. The article focuses on the topics: Symbolic programming.
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TL;DR: In this article, a generalization of the perturbative Landau gauge has been proposed for non-Abelian Yang-Mills theories and its implementation is discussed for two example methods, lattice gauge theory and the quantum equations of motion.
154 citations
TL;DR: In this paper, a generalization of the perturbative Landau gauge is proposed to describe gauge bosons beyond perturbation theory, and their implementation is discussed for two example methods, lattice gauge theory and quantum equations of motion.
Abstract: Gauge theories of the Yang-Mills type are the single most important building block of the standard model and beyond. Since Yang-Mills theories are gauge theories their elementary particles, the gauge bosons, cannot be described without fixing a gauge. Beyond perturbation theory, gauge-fixing in non-Abelian gauge theories is obstructed by the Gribov-Singer ambiguity. The construction and implementation of a method-independent gauge-fixing prescription to resolve this ambiguity is the most important step to describe gauge bosons beyond perturbation theory. Proposals for such a procedure, generalizing the perturbative Landau gauge, are described here. Their implementation are discussed for two example methods, lattice gauge theory and the quantum equations of motion. The most direct access to the properties of the gauge bosons is provided by their correlation functions. The corresponding two- and three-point correlation functions are presented at all energy scales. These give access to the properties of the gauge bosons, like their absence from the asymptotic physical state space, the absence of an on-shell mass pole, particle-like properties at high energies, and their running couplings. Furthermore, auxiliary degrees of freedom are introduced during gauge-fixing, and their properties are discussed as well. These results are presented for two, three, and four dimensions, and for various gauge algebras. Finally, the modifications of the properties of gauge bosons at finite temperature are presented. Evidence is provided that these reflect the phase structure of Yang-Mills theory. However, it is found that the phase transition is not deconfining the gauge bosons, although the bulk thermodynamical behavior is of a Stefan-Boltzmann type. The resolution of this apparent contradiction is also presented. This resolution also provides an explicit and constructive solution to the Linde problem.
122 citations
TL;DR: In this article, the results of correlation functions in the Landau gauge obtained from their equations of motions are discussed and compared to the results obtained in other covariant and maximally Abelian gauges.
90 citations
TL;DR: In this paper, the ghost and gluon propagators of Landau gauge Yang-Mills theory were solved and the ghost-gluon vertex was included in the truncation scheme for functional equations.
Abstract: We solve the Dyson-Schwinger equations of the ghost and gluon propagators of Landau gauge Yang-Mills theory together with that of the ghost-gluon vertex. The latter plays a central role in many truncation schemes for functional equations. By including it dynamically we can determine its influence on the propagators. We also suggest a new model for the three-gluon vertex motivated by lattice data which plays a crucial role to obtain stable solutions when the ghost-gluon vertex is included. We find that both vertices have a sizable quantitative impact on the mid-momentum regime and contribute to the reduction of the gap between lattice and Dyson-Schwinger equation results. Furthermore, we establish that the three-gluon vertex dressing turns negative at low momenta as suggested by lattice results in three dimensions.
71 citations
TL;DR: The Mathematica application DoFun is presented which allows to derive Dyson-Schwinger equations and renormalization group ow equations for n-point functions in a simple manner.
68 citations
References
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TL;DR: In this article, a modern pedagogic introduction to the ideas and techniques of quantum field theory is presented, with a brief overview of particle physics and a survey of relativistic wave equations and Lagrangian methods.
Abstract: This book is a modern pedagogic introduction to the ideas and techniques of quantum field theory. After a brief overview of particle physics and a survey of relativistic wave equations and Lagrangian methods, the quantum theory of scalar and spinor fields, and then of gauge fields, is developed. The emphasis throughout is on functional methods, which have played a large part in modern field theory. The book concludes with a brief survey of 'topological' objects in field theory and, new to this edition, a chapter devoted to supersymmetry.
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TL;DR: Mathematica has defined the state of the art in technical computing for over a decade, and has become a standard in many of the world's leading companies and universities as discussed by the authors.
Abstract: From the Publisher:
Mathematica has defined the state of the art in technical computing for over a decade, and has become a standard in many of the world's leading companies and universities From simple calculator operations to large-scale programming and the preparation of interactive documents, Mathematica is the tool of choice
3,566 citations
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01 Jan 1996
TL;DR: From the Publisher: Mathematica has defined the state of the art in technical computing for over a decade, and has become a standard in many of the world's leading companies and universities.
Abstract: From the Publisher:
Mathematica has defined the state of the art in technical computing for over a decade, and has become a standard in many of the world's leading companies and universities. From simple calculator operations to large-scale programming and the preparation of interactive documents, Mathematica is the tool of choice.
3,115 citations
"Algorithmic derivation of Dyson-Sch..." refers methods in this paper
...The algorithm explained in Section 2 is perfectly suitable for an implementation into a symbolic programming language like Mathematica [22]....
[...]
TL;DR: The ALPGEN as discussed by the authors event generator performs the calculation of exact matrix elements for a large set of parton-level processes of interest in the study of the Tevatron and LHC data.
Abstract: This paper presents a new event generator, ALPGEN, dedicated to the study of multiparton hard processes in hadronic collisions. The code performs, at the leading order in QCD and EW interactions, the calculation of the exact matrix elements for a large set of parton-level processes of interest in the study of the Tevatron and LHC data. The current version of the code describes the following final states: (W→f')Q+N jets (Q being a heavy quark, and f = l,q), with N ≤ 4;(Z/γ*→f)Q+N jets (f = l,ν), with N ≤ 4; W→f')+charm+N jets (f = l,q,N ≤ 5;W→f')+N jets (f = l,q and Z/γ*→f)+N jets (f = l,ν), with N ≤ 6; nW+mZ+lH+N jets, with n+m+l+N ≤ 8, N ≤ 3, including all 2-fermion decay modes of W and Z bosons, with spin correlations; Q+N jets, with t→bf' decays and relative spin correlations included where relevant, and N ≤ 6; QQ''+N jets, with Q and Q' heavy quarks (possibly equal) and N ≤ 4; HQ+N jets, with t→bf' decays and relative spin correlations included where relevant and N ≤ 4; N jets, with N ≤ 6. Parton-level events are generated, providing full information on their colour and flavour structure, enabling the evolution of the partons into fully hadronised final states.
1,828 citations
TL;DR: The Mathematica package FeynArts as discussed by the authors is used for the generation and visualization of Feynman diagrams and amplitudes, with three levels, user-defined model files, and support for supersymmetric models.
1,796 citations