Out-of-time-order asymptotic observables are quasi-isomorphic to time-ordered amplitudes
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arXiv
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| Natura: | Preprint |
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2024
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| _version_ | 1866917764019519488 |
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| author | Borsten, Leron Jonsson, Simon Kim, Hyungrok |
| author_facet | Borsten, Leron Jonsson, Simon Kim, Hyungrok |
| contents | Asymptotic observables in quantum field theory beyond the familiar $S$-matrix have recently attracted much interest, for instance in the context of gravity waveforms. Such observables can be understood in terms of Schwinger-Keldysh-type 'amplitudes' computed by a set of modified Feynman rules involving cut internal legs and external legs labelled by time-folds.
In parallel, a homotopy-algebraic understanding of perturbative quantum field theory has emerged in recent years. In particular, passing through homotopy transfer, the $S$-matrix of a perturbative quantum field theory can be understood as the minimal model of an associated (quantum) $L_\infty$-algebra.
Here we bring these two developments together. In particular, we show that Schwinger-Keldysh amplitudes are naturally encoded in an $L_\infty$-algebra, similar to ordinary scattering amplitudes. As before, they are computed via homotopy transfer, but using deformation-retract data that are not canonical (in contrast to the conventional $S$-matrix). We further show that the $L_\infty$-algebras encoding Schwinger-Keldysh amplitudes and ordinary amplitudes are quasi-isomorphic (meaning, in a suitable sense, equivalent). This entails a set of recursion relations that enable one to compute Schwinger-Keldysh amplitudes in terms of ordinary amplitudes or vice versa. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_11110 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Out-of-time-order asymptotic observables are quasi-isomorphic to time-ordered amplitudes Borsten, Leron Jonsson, Simon Kim, Hyungrok High Energy Physics - Theory Mathematical Physics 81T18 (Primary) 17B55, 18G50 (Secondary) Asymptotic observables in quantum field theory beyond the familiar $S$-matrix have recently attracted much interest, for instance in the context of gravity waveforms. Such observables can be understood in terms of Schwinger-Keldysh-type 'amplitudes' computed by a set of modified Feynman rules involving cut internal legs and external legs labelled by time-folds. In parallel, a homotopy-algebraic understanding of perturbative quantum field theory has emerged in recent years. In particular, passing through homotopy transfer, the $S$-matrix of a perturbative quantum field theory can be understood as the minimal model of an associated (quantum) $L_\infty$-algebra. Here we bring these two developments together. In particular, we show that Schwinger-Keldysh amplitudes are naturally encoded in an $L_\infty$-algebra, similar to ordinary scattering amplitudes. As before, they are computed via homotopy transfer, but using deformation-retract data that are not canonical (in contrast to the conventional $S$-matrix). We further show that the $L_\infty$-algebras encoding Schwinger-Keldysh amplitudes and ordinary amplitudes are quasi-isomorphic (meaning, in a suitable sense, equivalent). This entails a set of recursion relations that enable one to compute Schwinger-Keldysh amplitudes in terms of ordinary amplitudes or vice versa. |
| title | Out-of-time-order asymptotic observables are quasi-isomorphic to time-ordered amplitudes |
| topic | High Energy Physics - Theory Mathematical Physics 81T18 (Primary) 17B55, 18G50 (Secondary) |
| url | https://arxiv.org/abs/2405.11110 |