We report on the well-posedness of the Feynman problem for the Klein–Gordon equation on asymptotically Minkowski spacetimes. The main result is the invertibility of the Klein–Gordon operator with Feynman conditions at infinite times. Furthermore, the inverse is shown to coincide with the Duistermaat–Hörmander Feynman parametrix modulo smoothing terms.
DOI: 10.5802/slsedp.140
@article{SLSEDP_2019-2020____A3_0,
author = {Christian G\'erard and Micha{\l} Wrochna},
title = {The {Feynman} problem for the {Klein{\textendash}Gordon} equation},
journal = {S\'eminaire Laurent Schwartz {\textemdash} EDP et applications},
note = {talk:4},
publisher = {Institut des hautes \'etudes scientifiques & Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique},
year = {2019-2020},
doi = {10.5802/slsedp.140},
zbl = {1450.83003},
language = {en},
url = {https://slsedp.centre-mersenne.org/articles/10.5802/slsedp.140/}
}
TY - JOUR AU - Christian Gérard AU - Michał Wrochna TI - The Feynman problem for the Klein–Gordon equation JO - Séminaire Laurent Schwartz — EDP et applications N1 - talk:4 PY - 2019-2020 PB - Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique UR - https://slsedp.centre-mersenne.org/articles/10.5802/slsedp.140/ UR - https://zbmath.org/?q=an%3A1450.83003 UR - https://doi.org/10.5802/slsedp.140 DO - 10.5802/slsedp.140 LA - en ID - SLSEDP_2019-2020____A3_0 ER -
%0 Journal Article %A Christian Gérard %A Michał Wrochna %T The Feynman problem for the Klein–Gordon equation %J Séminaire Laurent Schwartz — EDP et applications %Z talk:4 %D 2019-2020 %I Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique %U https://doi.org/10.5802/slsedp.140 %R 10.5802/slsedp.140 %G en %F SLSEDP_2019-2020____A3_0
Christian Gérard; Michał Wrochna. The Feynman problem for the Klein–Gordon equation. Séminaire Laurent Schwartz — EDP et applications (2019-2020), Talk no. 4, 10 p. doi : 10.5802/slsedp.140. https://slsedp.centre-mersenne.org/articles/10.5802/slsedp.140/
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