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Algebraic field theory operads and linear quantization

Bruinsma, Simen; Schenkel, Alexander


Simen Bruinsma

Alexander Schenkel


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
Volume 109
Issue 11
Pages 2531-2570
Institution Citation Bruinsma, S., & Schenkel, A. (2019). Algebraic field theory operads and linear quantization. Letters in Mathematical Physics, 109(11), 2531-2570.
Keywords Algebraic quantum field theory; Locally covariant quantum field theory; Colored
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