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Title: Higher derivative scalar quantum field theory in curved spacetime

Abstract

We study a free scalar field $$\phi$$ in a fixed curved background spacetime subject to a higher derivative field equation of the form F($$\square)\phi$$ = 0 , where F is a polynomial of the form F($$\square$$) = $$Π_i(\square – m^2_i)$$ and all masses $$m_i$$ are distinct and real. Using an auxiliary field method to simplify the calculations, we obtain expressions for the Belinfante-Rosenfeld symmetric energy-momentum tensor and compare it with the canonical energy-momentum tensor when the background is Minkowski spacetime. We also obtain the conserved symplectic current necessary for quantization and briefly discuss the issue of negative energy vs negative norm and its relation to reflection positivity in Euclidean treatments. We study, without assuming spherical symmetry, the possible existence of finite energy static solutions of the scalar equations, in static or stationary background geometries. Subject to various assumptions on the potential, we establish nonexistence results including a no-scalar-hair theorem for static black holes. We consider Pais-Uhlenbeck field theories in a cosmological de Sitter background and show how the Hubble friction may eliminate what would otherwise be unstable behavior when interactions are included.

Authors:
ORCiD logo; ORCiD logo;
Publication Date:
Research Org.:
Texas A & M Univ., College Station, TX (United States)
Sponsoring Org.:
USDOE Office of Science (SC); European Research Council (ERC)
OSTI Identifier:
1574069
Alternate Identifier(s):
OSTI ID: 1802173
Grant/Contract Number:  
FG02-13ER42020; SC0010813; 694896
Resource Type:
Published Article
Journal Name:
Physical Review D
Additional Journal Information:
Journal Name: Physical Review D Journal Volume: 100 Journal Issue: 10; Journal ID: ISSN 2470-0010
Publisher:
American Physical Society
Country of Publication:
United States
Language:
English
Subject:
79 ASTRONOMY AND ASTROPHYSICS; Astronomy & Astrophysics; Physics

Citation Formats

Gibbons, G. W., Pope, C. N., and Solodukhin, Sergey. Higher derivative scalar quantum field theory in curved spacetime. United States: N. p., 2019. Web. doi:10.1103/PhysRevD.100.105008.
Gibbons, G. W., Pope, C. N., & Solodukhin, Sergey. Higher derivative scalar quantum field theory in curved spacetime. United States. https://doi.org/10.1103/PhysRevD.100.105008
Gibbons, G. W., Pope, C. N., and Solodukhin, Sergey. Wed . "Higher derivative scalar quantum field theory in curved spacetime". United States. https://doi.org/10.1103/PhysRevD.100.105008.
@article{osti_1574069,
title = {Higher derivative scalar quantum field theory in curved spacetime},
author = {Gibbons, G. W. and Pope, C. N. and Solodukhin, Sergey},
abstractNote = {We study a free scalar field $\phi$ in a fixed curved background spacetime subject to a higher derivative field equation of the form F($\square)\phi$ = 0 , where F is a polynomial of the form F($\square$) = $Π_i(\square – m^2_i)$ and all masses $m_i$ are distinct and real. Using an auxiliary field method to simplify the calculations, we obtain expressions for the Belinfante-Rosenfeld symmetric energy-momentum tensor and compare it with the canonical energy-momentum tensor when the background is Minkowski spacetime. We also obtain the conserved symplectic current necessary for quantization and briefly discuss the issue of negative energy vs negative norm and its relation to reflection positivity in Euclidean treatments. We study, without assuming spherical symmetry, the possible existence of finite energy static solutions of the scalar equations, in static or stationary background geometries. Subject to various assumptions on the potential, we establish nonexistence results including a no-scalar-hair theorem for static black holes. We consider Pais-Uhlenbeck field theories in a cosmological de Sitter background and show how the Hubble friction may eliminate what would otherwise be unstable behavior when interactions are included.},
doi = {10.1103/PhysRevD.100.105008},
journal = {Physical Review D},
number = 10,
volume = 100,
place = {United States},
year = {2019},
month = {11}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.1103/PhysRevD.100.105008

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Cited by: 1 work
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