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<p>This paper revisits the equivalence problem between algebraic quantum field theories and prefactorization algebras defined over globally hyperbolic Lorentzian manifolds. We develop a radically new approach whose main innovative features are 1.)&#xa0;a structural implementation of the additivity property used in earlier approaches and 2.)&#xa0;a reduction of the global equivalence problem to a family of simpler spacetime-wise problems. When applied to the case where the target category is a symmetric monoidal 1-category, this yields a generalization of the equivalence theorem from [Commun. Math. Phys. <b>377</b>, 971 (2019)]. In the case where the target is the symmetric monoidal <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\infty \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>∞</mi> </math></EquationSource> </InlineEquation>-category of cochain complexes, we obtain a reduction of the global <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\infty \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>∞</mi> </math></EquationSource> </InlineEquation>-categorical equivalence problem to simpler, but still challenging, spacetime-wise problems. The latter would be solved by showing that certain functors between 1-categories exhibit <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\infty \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>∞</mi> </math></EquationSource> </InlineEquation>-localizations; however, the available detection criteria are inconclusive in our case.</p>

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On the equivalence of AQFTs and prefactorization algebras

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年1月22日

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  • Marco Benini,
  • Victor Carmona,
  • Alastair Grant-Stuart,
  • Alexander Schenkel

摘要

This paper revisits the equivalence problem between algebraic quantum field theories and prefactorization algebras defined over globally hyperbolic Lorentzian manifolds. We develop a radically new approach whose main innovative features are 1.) a structural implementation of the additivity property used in earlier approaches and 2.) a reduction of the global equivalence problem to a family of simpler spacetime-wise problems. When applied to the case where the target category is a symmetric monoidal 1-category, this yields a generalization of the equivalence theorem from [Commun. Math. Phys. 377, 971 (2019)]. In the case where the target is the symmetric monoidal \(\infty \) ∞ -category of cochain complexes, we obtain a reduction of the global \(\infty \) ∞ -categorical equivalence problem to simpler, but still challenging, spacetime-wise problems. The latter would be solved by showing that certain functors between 1-categories exhibit \(\infty \) ∞ -localizations; however, the available detection criteria are inconclusive in our case.