Coloring Operads for Algebraic Field Theory

Simen Bruinsma

doi:10.1002/prop.201910004

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arXiv · 1903.02863

Coloring Operads for Algebraic Field Theory

Simen Bruinsma

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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.

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Simen Bruinsma. 2019-03-07. Coloring Operads for Algebraic Field Theory. https://doi.org/10.1002/prop.201910004

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