From operads and PROPs to Feynman Processes

2007/01/10 by Lucian M. Ionescu, Lucian M Ionescu, Ionescu, Lucian M
Mathematics · Physics and Astronomy · #18Dxx #81Qxx #Advanced Topics in Algebra #FOS: Mathematics #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories #Quantum Algebra (math.QA) #math-ph #math.MP #math.QA #msc:18Dxx #msc:81Qxx

paper · pdf · doi:10.48550/arxiv.math/0701299

15 pages

arxiv created 2007/01/10 · openalex publication_date 2007/01/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Operads and PROPs are presented, together with examples and applications to quantum physics suggesting the structure of Feynman categories/PROPs and the corresponding algebras.

Citations

• Topological field theories, string backgrounds and homotopy algebras
• 2D Quantum Gravity, Matrix Models and Graph Combinatorics
• Koszul duality for operads

Related

• Lectures on Feynman categories
• The props of quantum mechanics
• Modular operads and the quantum open-closed homotopy algebra
• Operads, homotopy theory and higher categories in algebraic quantum field theory
• Categories of Physical Processes