The QED beta-function from global solutions to Dyson-Schwinger equations
We discuss the structure of beta functions as determined by the recursive nature of Dyson--Schwinger equations turned into an analysis of ordinary differential equations, with particular emphasis given to quantum electrodynamics. In particular we determine when a separatrix for solutions to such ODE...
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| creator | Guillaume van Baalen Kreimer, Dirk Uminsky, David Yeats, Karen |
| description | We discuss the structure of beta functions as determined by the recursive nature of Dyson--Schwinger equations turned into an analysis of ordinary differential equations, with particular emphasis given to quantum electrodynamics. In particular we determine when a separatrix for solutions to such ODEs exists and clarify the existence of Landau poles beyond perturbation theory. Both are determined in terms of explicit conditions on the asymptotics for the growth of skeleton graphs. |
| doi_str_mv | 10.48550/arxiv.0805.0826 |
| format | Article |
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| language | eng |
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| source | Ejournal Publishers (free content); arXiv.org |
| subjects | Differential equations Mathematical analysis Mathematics - Mathematical Physics Ordinary differential equations Perturbation theory Physics - High Energy Physics - Phenomenology Physics - High Energy Physics - Theory Physics - Mathematical Physics Quantum electrodynamics Quantum theory |
| title | The QED beta-function from global solutions to Dyson-Schwinger equations |
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