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Algebraic field theory operads and linear quantization

Bruinsma, Simen; Schenkel, Alexander

Authors

Simen Bruinsma

Alexander Schenkel

Abstract

We generalize the operadic approach to algebraic quantum field theory (arXiv:1709.08657) to a broader class of field theories whose observables on a spacetime are algebras over any single-colored operad. A novel feature of our framework is that it gives rise to adjunctions between different types of field theories. As an interesting example, we study an adjunction whose left adjoint describes the quantization of linear field theories. We also analyze homotopical properties of the linear quantization adjunction for chain complex valued field theories, which leads to a homotopically meaningful quantization prescription for linear gauge theories.

Journal Article Type Article
Publication Date Jul 9, 2019
Journal Letters in Mathematical Physics
Print ISSN 0377-9017
Electronic ISSN 1573-0530
Publisher Springer Verlag
Peer Reviewed Peer Reviewed
DOI https://doi.org/10.1007/s11005-019-01195-7
Keywords Algebraic quantum field theory; Locally covariant quantum field theory; Colored
Publisher URL https://link.springer.com/article/10.1007%2Fs11005-019-01195-7
Additional Information Received: 27 September 2018; Revised: 30 April 2019; Accepted: 3 July 2019; First Online: 9 July 2019; : ; : On behalf of all authors, the corresponding author states that there is no conflict of interest.

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