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Classical and quantum scattering of massive Klein--Gordon fields in asymptotically flat spacetimes
Abstract
We use microlocal tools to define distinguished incoming and outgoing vacuum states of the quantum theory of massive Klein--Gordon fields in non-trapping asymptotically flat spacetimes, including radiative perturbations of Minkowski space. The asymptotic vacuum states satisfy the Hadamard condition, and the incoming and outgoing particle representations are unitarily equivalent, or in other words the quantum S-matrix is well-defined. These results are based on a description of scattering of classical fields which keeps track of the asymptotic distinction between positive- and negative-frequency solutions of the Klein--Gordon equation. Our emphasis is on developing the theory without recourse to explicit asymptotics for classical waves.
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BibTeX
@misc{molodyk2026classical,
title = {{Classical and quantum scattering of massive Klein--Gordon fields in asymptotically flat spacetimes}},
author = {Mikhail Molodyk},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.17819},
eprint = {2610.17819},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.17819},
}
RIS
TY - UNPB
TI - Classical and quantum scattering of massive Klein--Gordon fields in asymptotically flat spacetimes
AU - Mikhail Molodyk
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.17819
UR - https://arxiv.org/abs/2610.17819
AB - We use microlocal tools to define distinguished incoming and outgoing vacuum states of the quantum theory of massive Klein--Gordon fields in non-trapping asymptotically flat spacetimes, including radiative perturbations of Minkowski space. The asymptotic vacuum states satisfy the Hadamard condition, and the incoming and outgoing particle representations are unitarily equivalent, or in other words the quantum S-matrix is well-defined. These results are based on a description of scattering of classical fields which keeps track of the asymptotic distinction between positive- and negative-frequency solutions of the Klein--Gordon equation. Our emphasis is on developing the theory without recourse to explicit asymptotics for classical waves.
ER -