Adiabatic Ground States in Non-smooth Spacetimes

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Autoren

  • Yafet Sanchez Sanchez
  • Elmar Schrohe

Organisationseinheiten

Forschungs-netzwerk anzeigen

Details

OriginalspracheEnglisch
Seiten (von - bis)2929–2948
Seitenumfang20
FachzeitschriftAnnales Henri Poincare
Jahrgang24
Ausgabenummer9
Frühes Online-Datum30 März 2023
PublikationsstatusVeröffentlicht - Sept. 2023

Abstract

Ground states are a well-known class of Hadamard states in smooth spacetimes. In this paper we show that the ground state of the Klein-Gordon field in a non-smooth ultrastatic spacetime is an adiabatic state. The order of the state depends linearly on the regularity of the metric. We obtain the result by combining microlocal estimates for the causal propagator, propagation of singularities results for non-smooth pseudodifferential operators, and eigenvalue asymptotics for elliptic operators of low regularity.

ASJC Scopus Sachgebiete

Zitieren

Adiabatic Ground States in Non-smooth Spacetimes. / Sanchez Sanchez, Yafet; Schrohe, Elmar.
in: Annales Henri Poincare, Jahrgang 24, Nr. 9, 09.2023, S. 2929–2948.

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Sanchez Sanchez Y, Schrohe E. Adiabatic Ground States in Non-smooth Spacetimes. Annales Henri Poincare. 2023 Sep;24(9):2929–2948. Epub 2023 Mär 30. doi: 10.48550/arXiv.2207.01429, 10.1007/s00023-023-01280-7
Sanchez Sanchez, Yafet ; Schrohe, Elmar. / Adiabatic Ground States in Non-smooth Spacetimes. in: Annales Henri Poincare. 2023 ; Jahrgang 24, Nr. 9. S. 2929–2948.
Download
@article{1673ef79605b46e18c0926d7669e4a9f,
title = "Adiabatic Ground States in Non-smooth Spacetimes",
abstract = "Ground states are a well-known class of Hadamard states in smooth spacetimes. In this paper we show that the ground state of the Klein-Gordon field in a non-smooth ultrastatic spacetime is an adiabatic state. The order of the state depends linearly on the regularity of the metric. We obtain the result by combining microlocal estimates for the causal propagator, propagation of singularities results for non-smooth pseudodifferential operators, and eigenvalue asymptotics for elliptic operators of low regularity.",
keywords = "math-ph, math.MP",
author = "{Sanchez Sanchez}, Yafet and Elmar Schrohe",
note = "Open Access funding enabled and organized by Projekt DEAL.",
year = "2023",
month = sep,
doi = "10.48550/arXiv.2207.01429",
language = "English",
volume = "24",
pages = "2929–2948",
journal = "Annales Henri Poincare",
issn = "1424-0637",
publisher = "Birkhauser Verlag Basel",
number = "9",

}

Download

TY - JOUR

T1 - Adiabatic Ground States in Non-smooth Spacetimes

AU - Sanchez Sanchez, Yafet

AU - Schrohe, Elmar

N1 - Open Access funding enabled and organized by Projekt DEAL.

PY - 2023/9

Y1 - 2023/9

N2 - Ground states are a well-known class of Hadamard states in smooth spacetimes. In this paper we show that the ground state of the Klein-Gordon field in a non-smooth ultrastatic spacetime is an adiabatic state. The order of the state depends linearly on the regularity of the metric. We obtain the result by combining microlocal estimates for the causal propagator, propagation of singularities results for non-smooth pseudodifferential operators, and eigenvalue asymptotics for elliptic operators of low regularity.

AB - Ground states are a well-known class of Hadamard states in smooth spacetimes. In this paper we show that the ground state of the Klein-Gordon field in a non-smooth ultrastatic spacetime is an adiabatic state. The order of the state depends linearly on the regularity of the metric. We obtain the result by combining microlocal estimates for the causal propagator, propagation of singularities results for non-smooth pseudodifferential operators, and eigenvalue asymptotics for elliptic operators of low regularity.

KW - math-ph

KW - math.MP

UR - http://www.scopus.com/inward/record.url?scp=85151446694&partnerID=8YFLogxK

U2 - 10.48550/arXiv.2207.01429

DO - 10.48550/arXiv.2207.01429

M3 - Article

VL - 24

SP - 2929

EP - 2948

JO - Annales Henri Poincare

JF - Annales Henri Poincare

SN - 1424-0637

IS - 9

ER -