Algebraic field theory operads and linear quantization

Bruinsma, Simen; Schenkel, Alexander

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.

Citation

Bruinsma, S., & Schenkel, A. (2019). Algebraic field theory operads and linear quantization. Letters in Mathematical Physics, 109(11), 2531-2570. https://doi.org/10.1007/s11005-019-01195-7

• Journal Article Type: Article
• Acceptance Date: Jul 2, 2019
• Online Publication Date: Jul 9, 2019
• Publication Date: Nov 1, 2019
• Deposit Date: Jul 11, 2019
• Publicly Available Date: Jul 10, 2020
• 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
• DOI: https://doi.org/10.1007/s11005-019-01195-7
• Keywords: Algebraic quantum field theory; Locally covariant quantum field theory; Colored
• Public URL: https://nottingham-repository.worktribe.com/output/2299121
• Publisher URL: https://link.springer.com/article/10.1007%2Fs11005-019-01195-7
• Contract Date: Jul 11, 2019