Abstract
We prove essential self-adjointness of the spatial part of the linear Klein-Gordon operator with external potential for a large class of globally hyperbolic manifolds. The proof is conducted by a fusion of new results concerning globally hyperbolic manifolds, the theory of weighted Hilbert spaces and related functional analytic advances.
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Acknowledgments
The authors would like to thank Suzanne Lanéry for many useful discussions and one of the authors (AM) would like to thank Bernard Kay for enlightening and interesting discussions on quantum field theory in curved spacetimes and related functional analytical questions. The authors acknowledge partial support from CONACYT project 259258.
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Much, A., Oeckl, R. Self-Adjointness in Klein-Gordon Theory on Globally Hyperbolic Spacetimes. Math Phys Anal Geom 24, 5 (2021). https://doi.org/10.1007/s11040-021-09379-1
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DOI: https://doi.org/10.1007/s11040-021-09379-1