CrasyDSE: a framework for solving Dyson-Schwinger equations. (English) Zbl 1302.81004

Huber, Markus Q.; Mitter, Mario

Comput. Phys. Commun. 183, No. 11, 2441-2457 (2012).

Summary: Dyson-Schwinger equations are important tools for non-perturbative analyses of quantum field theories. For example, they are very useful for investigations in quantum chromodynamics and related theories. However, sometimes progress is impeded by the complexity of the equations. Thus automating parts of the calculations will certainly be helpful in future investigations. In this article we present a framework for such an automation based on a \(C++\) code that can deal with a large number of Green functions. Since also the creation of the expressions for the integrals of the Dyson-Schwinger equations needs to be automated, we defer this task to a \(Mathematica\) notebook. We illustrate the complete workflow with an example from Yang-Mills theory coupled to a fundamental scalar field that has been investigated recently. As a second example we calculate the propagators of pure Yang-Mills theory. Our code can serve as a basis for many further investigations where the equations are too complicated to tackle by hand. It also can easily be combined with \(DoFun\), a program for the derivation of Dyson-Schwinger equations.

MSC:

81-04	Software, source code, etc. for problems pertaining to quantum theory
81-08	Computational methods for problems pertaining to quantum theory
81T80	Simulation and numerical modelling (quantum field theory) (MSC2010)
81P40	Quantum coherence, entanglement, quantum correlations
81T13	Yang-Mills and other gauge theories in quantum field theory

Keywords:

Dyson-Schwinger equations; correlation functions; quantum field theory

Software:

CrasyDSE; Mathematica

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