Higher-derivative Lagrangians, nonlocality, problems, and solutions
Abstract
Higher-derivative theories are frequently avoided because of undesirable properties, yet they occur naturally as corrections to general relativity and cosmic strings. We discuss some of their more interesting and disturbing problems, with examples. A natural method of removing all the problems of higher derivatives is reviewed. This method of "perturbative constraints" is required for at least one class of higher-derivative theories---those which are associated with nonlocality. Nonlocality often appears in low-energy theories described by effective actions. The method may also be applied to a wide class of other higher-derivative theories. An example system is solved, exactly and perturbatively, for which the perturbative solutions approximate the exact solutions only when the method of "perturbative constraints" is employed. Ramifications for corrections to general relativity, cosmic strings with rigidity terms, and other higher-derivative theories are explored.
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For closed spacetimes, the proper quantity to subtract using the adiabatic method should be constructed from mode solutions with a continuum measure instead of a discrete one.
“It has been argued that in such situations, the proper quantity to subtract using the adiabatic method should still be constructed from mode solutions with a continuum measure instead of a discrete one [36].”
From Stress-energy tensor of a scalar field on a product spacetime with a time-dependent compact dimension (2026) · cites this paper as [36]
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References 35 · Cited by 432
- Authors
- Simon, J. Z.
- Affiliations
- University of California, Santa Barbara (US)
- Corresponding author
- Simon, Jonathan Z.
- ORCID
- Simon, Jonathan Z.
- Venue
- Physical Review D
- Publisher
- American Physical Society (APS)
- Published
- 1990-06-15
- Volume
- 41
- Issue
- 12
- Pages
- 3720-3733
- ISSN
- 0556-2821 (ISSN-L)
- OpenAlex
- W2170609994
- Cited by
- 432
- References
- 35
- Citations by year
- 2026: 7 · 2025: 9 · 2024: 7 · 2023: 11 · 2022: 12 · 2021: 41 · 2020: 43 · 2019: 17 · 2018: 20 · 2017: 14 · 2016: 18 · 2015: 20 · 2014: 9 · 2013: 13 · 2012: 12
- FWCI
- 14.54
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields (publishedVersion)
- PubMed (publishedVersion)
- Funders
- National Science Foundation
- Topics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Cosmology and Gravitation Theories
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Keywords
- higher-derivative theories, nonlocality, effective action, cosmic strings, exact solutions, perturbation solution, effective field theory
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