New Classes of Solutions for Euclidean Scalar Field Theories Article Swipe
Carl M. Bender
,
Sarben Sarkar
·
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.3390/universe10020072
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.3390/universe10020072
This paper presents new classes of exact radial solutions to the nonlinear ordinary differential equation that arises as a saddle-point condition for a Euclidean scalar field theory in D-dimensional spacetime. These solutions are found by exploiting the dimensional consistency of the radial differential equation for a single massless scalar field, which allows it to transform into an autonomous equation. For massive theories, the radial equation is not exactly solvable, but the massless solutions provide useful approximations to the results for the massive case. The solutions presented here depend on the power of the interaction and on the spatial dimension, both of which may be noninteger. Scalar equations arising in the study of conformal invariance fit into this framework, and classes of new solutions are found. These solutions exhibit two distinct behaviors as D→2 from above.
Related Topics
Concepts
Physics
Euclidean geometry
Theoretical physics
Scalar theories of gravitation
Scalar field
Scalar field theory
Scalar (mathematics)
Mathematical physics
Field (mathematics)
Field theory (psychology)
Classical mechanics
Classical field theory
Quantum mechanics
General relativity
Quantum gravity
Pure mathematics
Geometry
Quantum
Mathematics
Metadata
- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.3390/universe10020072
- https://www.mdpi.com/2218-1997/10/2/72/pdf?version=1706871462
- OA Status
- gold
- Cited By
- 2
- References
- 43
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4391470570
All OpenAlex metadata
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https://doi.org/10.3390/universe10020072Digital Object Identifier
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New Classes of Solutions for Euclidean Scalar Field TheoriesWork title
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articleOpenAlex work type
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enPrimary language
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2024Year of publication
- Publication date
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2024-02-02Full publication date if available
- Authors
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Carl M. Bender, Sarben SarkarList of authors in order
- Landing page
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https://doi.org/10.3390/universe10020072Publisher landing page
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https://www.mdpi.com/2218-1997/10/2/72/pdf?version=1706871462Direct link to full text PDF
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YesWhether a free full text is available
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goldOpen access status per OpenAlex
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https://www.mdpi.com/2218-1997/10/2/72/pdf?version=1706871462Direct OA link when available
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Physics, Euclidean geometry, Theoretical physics, Scalar theories of gravitation, Scalar field, Scalar field theory, Scalar (mathematics), Mathematical physics, Field (mathematics), Field theory (psychology), Classical mechanics, Classical field theory, Quantum mechanics, General relativity, Quantum gravity, Pure mathematics, Geometry, Quantum, MathematicsTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
2Total citation count in OpenAlex
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2025: 1, 2024: 1Per-year citation counts (last 5 years)
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10Other works algorithmically related by OpenAlex
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