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arXiv · 1306.3220

Classical 3-loop 2-body diagrams

Barak Kol·Ruth Shir
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Abstract

As part of the study of the two-body problem in Einstein's gravity, the fourth post-Newtonian order (4PN) of the two-body effective action is being computed presently by both effective field theory (EFT) methods and others. Diagrams with 3 (or 4) classical loops appear to be a significant obstacle. In this paper we develop a method to compute such 3-loop diagrams and demonstrate it through a specific diagram. We reduce the classical diagrams through shrinking the body worldlines to a form more familiar in Quantum Field Theory. A key ingredient in the evaluation is the Integration By Parts method for Feynman integrals.

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Barak Kol, Ruth Shir. 2013-06-13. Classical 3-loop 2-body diagrams. https://doi.org/10.1007/jhep09(2013)069

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