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Relating Nets and Factorization Algebras of Observables: Free Field Theories

Abstract
In this paper we relate two mathematical frameworks that make perturbative quantum field theory rigorous: perturbative algebraic quantum field theory (pAQFT) and the factorization algebras framework developed by Costello and Gwilliam. To make the comparison as explicit as possible, we use the free scalar field as our running example, while giving proofs that apply to any field theory whose equations of motion are Greenhyperbolic (which includes, for instance, free fermions). The main claim is that for such free theories, there is a natural transformation intertwining the two constructions. In fact, both approaches encode equivalent information if one assumes the time-slice axiom. The key technical ingredient is to use time-ordered products as an intermediate step between a net of associative algebras and a factorization algebra.
Type
article
article
Date
2020-01-01
Publisher
Degree
Advisors
Rights
UMass Amherst Open Access Policy
License
http://creativecommons.org/licenses/by/4.0/