The Klein-Gordon equation on asymptotically Minkowski spacetimes: the Feynman propagator
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908430350942208 |
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| author | Baskin, Dean Doll, Moritz Gell-Redman, Jesse |
| author_facet | Baskin, Dean Doll, Moritz Gell-Redman, Jesse |
| contents | We develop a theory of Feynman propagators for the massive Klein--Gordon equation with asymptotically static perturbations. Building on our previous work on the causal propagators, we employ a framework based on propagation of singularities estimates in Vasy's 3sc-calculus. We combine these estimates to prove global spacetime mapping properties for the Feynman propagator, and to show that it satisfies a microlocal Hadamard condition.
We show that the Feynman propagator can be realized as the inverse of a mapping between appropriate $L^2$-based Sobolev spaces with additional regularity near the asymptotic sources of the Hamiltonian flow, realized as a family of radial points on a compactified spacetime. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_01600 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Klein-Gordon equation on asymptotically Minkowski spacetimes: the Feynman propagator Baskin, Dean Doll, Moritz Gell-Redman, Jesse Analysis of PDEs Mathematical Physics Functional Analysis We develop a theory of Feynman propagators for the massive Klein--Gordon equation with asymptotically static perturbations. Building on our previous work on the causal propagators, we employ a framework based on propagation of singularities estimates in Vasy's 3sc-calculus. We combine these estimates to prove global spacetime mapping properties for the Feynman propagator, and to show that it satisfies a microlocal Hadamard condition. We show that the Feynman propagator can be realized as the inverse of a mapping between appropriate $L^2$-based Sobolev spaces with additional regularity near the asymptotic sources of the Hamiltonian flow, realized as a family of radial points on a compactified spacetime. |
| title | The Klein-Gordon equation on asymptotically Minkowski spacetimes: the Feynman propagator |
| topic | Analysis of PDEs Mathematical Physics Functional Analysis |
| url | https://arxiv.org/abs/2507.01600 |