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.
- 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}
}
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https://doi.org/10.1103/PhysRevD.100.105008
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