2017/11/17 by Owen Gwilliam, Kasia Rejzner, Gwilliam, Owen +1 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Category Theory (math.CT) #FOS: Mathematics #FOS: Physical sciences #Logic, programming, and type systems #Mathematical Physics (math-ph) #Quantum Mechanics and Applications
paper · pdf · doi:10.48550/arxiv.1711.06674
openalex publication_date 2017/11/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we relate two mathematical frameworks that make perturbative\nquantum field theory rigorous: perturbative algebraic quantum field theory\n(pAQFT) and the factorization algebras framework developed by Costello and\nGwilliam. To make the comparison as explicit as possible, we use the free\nscalar field as our running example, while giving proofs that apply to any\nfield theory whose equations of motion are Green-hyperbolic (which includes,\nfor instance, free fermions). The main claim is that for such free theories,\nthere is a natural transformation intertwining the two constructions. In fact,\nboth approaches encode equivalent information if one assumes the time-slice\naxiom. The key technical ingredient is to use time-ordered products as an\nintermediate step between a net of associative algebras and a factorization\nalgebra.\n