The Feynman propagator for massive Klein-Gordon fields on radiative asymptotically flat spacetimes
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911228367994880 |
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| author | Molodyk, Mikhail Vasy, András |
| author_facet | Molodyk, Mikhail Vasy, András |
| contents | On a large class of asymptotically flat spacetimes which includes radiative perturbations of Minkowski space, we define a distinguished global Feynman propagator for massive Klein-Gordon fields by means of the microlocal approach to non-elliptic Fredholm theory, working in the de,sc-pseudodifferential algebra due to Sussman. We extend the limiting absorption principle (the "$i\varepsilon$ prescription" for the Feynman propagator) to this setting. Motivated by the complicated Hamilton flow structure arising in this problem, we also prove a new localized radial point estimate in the spirit of Haber-Vasy which, under appropriate nondegeneracy assumptions, allows one to propagate microlocal regularity into a single radial point belonging to a larger radial set which can be a source, sink, or saddle for the Hamilton flow. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_04308 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Feynman propagator for massive Klein-Gordon fields on radiative asymptotically flat spacetimes Molodyk, Mikhail Vasy, András General Relativity and Quantum Cosmology Mathematical Physics Analysis of PDEs 35L05, 58J40, 81T20 On a large class of asymptotically flat spacetimes which includes radiative perturbations of Minkowski space, we define a distinguished global Feynman propagator for massive Klein-Gordon fields by means of the microlocal approach to non-elliptic Fredholm theory, working in the de,sc-pseudodifferential algebra due to Sussman. We extend the limiting absorption principle (the "$i\varepsilon$ prescription" for the Feynman propagator) to this setting. Motivated by the complicated Hamilton flow structure arising in this problem, we also prove a new localized radial point estimate in the spirit of Haber-Vasy which, under appropriate nondegeneracy assumptions, allows one to propagate microlocal regularity into a single radial point belonging to a larger radial set which can be a source, sink, or saddle for the Hamilton flow. |
| title | The Feynman propagator for massive Klein-Gordon fields on radiative asymptotically flat spacetimes |
| topic | General Relativity and Quantum Cosmology Mathematical Physics Analysis of PDEs 35L05, 58J40, 81T20 |
| url | https://arxiv.org/abs/2510.04308 |