On the relation between functorial quantum field theory (axiomatizing the Schrödinger picture of quantum field theory) and algebraic quantum field theory (axiomatizing the Heisenberg picture):
Urs Schreiber, AQFT from n-Functorial QFT, Comm. Math. Phys. 291 2 (2009) 357-401 [doi:10.1007/s00220-009-0840-2, arXiv:0806.1079]
Theo Johnson-Freyd: Heisenberg-picture quantum field theory, in: Representation Theory, Mathematical Physics, and Integrable Systems, Progress in Mathematics 340 (2021) [doi:10.1007/978-3-030-78148-4_13, arXiv:1508.05908]
Severin Bunk, James MacManus, Alexander Schenkel: Lorentzian bordisms in algebraic quantum field theory, Lett. Math. Phys. 115 16 (2025) [doi:10.1007/s11005-025-01906-3, arXiv:2308.01026]
Severin Bunk, James MacManus, Alexander Schenkel: An equivalence theorem for algebraic and functorial QFT [arXiv:2504.15759]
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