Likelihood Equations and Scattering Amplitudes
| Autor: | Bernd Sturmfels, Simon Telen |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
High Energy Physics - Theory
Mathematics - Algebraic Geometry Complementary and alternative medicine High Energy Physics - Theory (hep-th) FOS: Mathematics Pharmaceutical Science FOS: Physical sciences Pharmacology (medical) Mathematics - Statistics Theory Statistics Theory (math.ST) Algebraic Geometry (math.AG) |
| DOI: | 10.48550/arxiv.2012.05041 |
| Popis: | We relate scattering amplitudes in particle physics to maximum likelihood estimation for discrete models in algebraic statistics. The scattering potential plays the role of the log-likelihood function, and its critical points are solutions to rational function equations. We study the ML degree of low-rank tensor models in statistics, and we revisit physical theories proposed by Arkani-Hamed, Cachazo and their collaborators. Recent advances in numerical algebraic geometry are employed to compute and certify critical points. We also discuss positive models and how to compute their string amplitudes. Comment: 18 pages |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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