The Analytic Wavefunction
Abstract The wavefunction in quantum field theory is an invaluable tool for tackling a variety of problems, including probing the interior of Minkowski spacetime and modelling boundary observables in de Sitter spacetime. Here we study the analytic structure of wavefunction coefficients in Minkowski...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2023-06-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP06(2023)020 |
| _version_ | 1797675879151697920 |
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| author | Santiago Agüí Salcedo Mang Hei Gordon Lee Scott Melville Enrico Pajer |
| author_facet | Santiago Agüí Salcedo Mang Hei Gordon Lee Scott Melville Enrico Pajer |
| author_sort | Santiago Agüí Salcedo |
| collection | DOAJ |
| description | Abstract The wavefunction in quantum field theory is an invaluable tool for tackling a variety of problems, including probing the interior of Minkowski spacetime and modelling boundary observables in de Sitter spacetime. Here we study the analytic structure of wavefunction coefficients in Minkowski as a function of their kinematics. We introduce an off-shell wavefunction in terms of amputated time-ordered correlation functions and show that it is analytic in the complex energy plane except for possible singularities on the negative real axis. These singularities are determined to all loop orders by a simple energy-conservation condition. We confirm this picture by developing a Landau analysis of wavefunction loop integrals and corroborate our findings with several explicit calculations in scalar field theories. This analytic structure allows us to derive new UV/IR sum rules for the wavefunction that fix the coefficients in its low-energy expansion in terms of integrals of discontinuities in the corresponding UV-completion. In contrast to the analogous sum rules for scattering amplitudes, the wavefunction sum rules can also constrain total-derivative interactions. We explicitly verify these new relations at one-loop order in simple UV models of a light and a heavy scalar. Our results, which apply to both Lorentz invariant and boost-breaking theories, pave the way towards deriving wavefunction positivity bounds in flat and cosmological spacetimes. |
| first_indexed | 2024-03-11T22:21:01Z |
| format | Article |
| id | doaj.art-7688c85daf4c44db9eb899d53f3d9947 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-03-11T22:21:01Z |
| publishDate | 2023-06-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-7688c85daf4c44db9eb899d53f3d99472023-09-24T11:05:54ZengSpringerOpenJournal of High Energy Physics1029-84792023-06-012023619010.1007/JHEP06(2023)020The Analytic WavefunctionSantiago Agüí Salcedo0Mang Hei Gordon Lee1Scott Melville2Enrico Pajer3Department of Applied Mathematics and Theoretical Physics, University of CambridgeDepartment of Applied Mathematics and Theoretical Physics, University of CambridgeDepartment of Applied Mathematics and Theoretical Physics, University of CambridgeDepartment of Applied Mathematics and Theoretical Physics, University of CambridgeAbstract The wavefunction in quantum field theory is an invaluable tool for tackling a variety of problems, including probing the interior of Minkowski spacetime and modelling boundary observables in de Sitter spacetime. Here we study the analytic structure of wavefunction coefficients in Minkowski as a function of their kinematics. We introduce an off-shell wavefunction in terms of amputated time-ordered correlation functions and show that it is analytic in the complex energy plane except for possible singularities on the negative real axis. These singularities are determined to all loop orders by a simple energy-conservation condition. We confirm this picture by developing a Landau analysis of wavefunction loop integrals and corroborate our findings with several explicit calculations in scalar field theories. This analytic structure allows us to derive new UV/IR sum rules for the wavefunction that fix the coefficients in its low-energy expansion in terms of integrals of discontinuities in the corresponding UV-completion. In contrast to the analogous sum rules for scattering amplitudes, the wavefunction sum rules can also constrain total-derivative interactions. We explicitly verify these new relations at one-loop order in simple UV models of a light and a heavy scalar. Our results, which apply to both Lorentz invariant and boost-breaking theories, pave the way towards deriving wavefunction positivity bounds in flat and cosmological spacetimes.https://doi.org/10.1007/JHEP06(2023)020Effective Field TheoriesBoundary Quantum Field TheoryScattering Amplitudes |
| spellingShingle | Santiago Agüí Salcedo Mang Hei Gordon Lee Scott Melville Enrico Pajer The Analytic Wavefunction Journal of High Energy Physics Effective Field Theories Boundary Quantum Field Theory Scattering Amplitudes |
| title | The Analytic Wavefunction |
| title_full | The Analytic Wavefunction |
| title_fullStr | The Analytic Wavefunction |
| title_full_unstemmed | The Analytic Wavefunction |
| title_short | The Analytic Wavefunction |
| title_sort | analytic wavefunction |
| topic | Effective Field Theories Boundary Quantum Field Theory Scattering Amplitudes |
| url | https://doi.org/10.1007/JHEP06(2023)020 |
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