The QCD beta-function from global solutions to Dyson-Schwinger equations
arXiv:0906.1754 · doi:10.1016/j.aop.2009.10.011
Abstract
We study quantum chromodynamics from the viewpoint of untruncated Dyson-Schwinger equations turned to an ordinary differential equation for the gluon anomalous dimension. This nonlinear equation is parameterized by a function P(x) which is unknown beyond perturbation theory. Still, very mild assumptions on P(x) lead to stringent restrictions for possible solutions to Dyson-Schwinger equations. We establish that the theory must have asymptotic freedom beyond perturbation theory and also investigate the low energy regime and the possibility for a mass gap in the asymptotically free theory.
34 pages, 4 figures
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Cited by in corpus (12)
- Non-Perturbative Completion of Hopf-Algebraic Dyson-Schwinger Equations
- Approximate Differential Equations for Renormalization Group Functions in Models Free of Vertex Divergencies
- Renormalization, Hopf algebras and Mellin transforms
- Resurgent transseries Dyson-Schwinger equations
- Algebraic Structures in local QFT
- Algebra for quantum fields
- Mulitgraded Dyson-Schwinger systems
- Hopf algebras and Dyson-Schwinger equations
- Feynman diagrams and their algebraic lattices
- Three Etudes in QFT
- Renormalization Hopf algebras for gauge theories and BRST-symmetries
- A mathematical perspective on the phenomenology of non-perturbative Quantum Field Theory