2019/03/07 by Simen Bruinsma
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebra over a field #Algebraic number #Algebraic structures and combinatorial models #Algebraic theory #Field (mathematics) #Field theory (psychology) #Functor #Homotopy and Cohomology in Algebraic Topology #Quantization (signal processing) #Quantum field theory #hep-th #math.AT
paper · pdf · doi:10.1002/prop.201910004
13 pages, Contribution to Proceedings of LMS/EPSRC Durham Symposium Higher Structures in M-Theory, August 2018
arxiv created 2019/03/07 · openalex created_date 2019/03/22 · openalex publication_date 2019/04/22 · arxiv updated 2021/07/28 · openalex updated_date 2026/08/05
Abstract In these proceedings we summarize previous work where we formalize a general concept of algebraic field theories using operads. After giving a gentle reminder of algebraic quantum field theory, operads and their algebras, we construct field theory operads, whose algebras are exactly algebraic field theories. Specifically, they satisfy a suitable version of the Einstein causality axiom. From this construction we get adjunctions between different types of field theories, including adjunctions related to local‐to‐global extensions and the time‐slice axiom, and a quantization functor for linear field theories that is compatible with these structures. We also take first steps towards a derived linear quantization functor.