English

Coloring Operads for Algebraic Field Theory

High Energy Physics - Theory 2021-07-28 v1 Algebraic Topology

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.

Keywords

Cite

@article{arxiv.1903.02863,
  title  = {Coloring Operads for Algebraic Field Theory},
  author = {Simen Bruinsma},
  journal= {arXiv preprint arXiv:1903.02863},
  year   = {2021}
}

Comments

13 pages, Contribution to Proceedings of LMS/EPSRC Durham Symposium Higher Structures in M-Theory, August 2018

R2 v1 2026-06-23T08:00:59.930Z