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Harmonic maps as models for physical theories
Abstract
Harmonic maps are an aesthetically appealing class of nonlinear field equations of which only a few nontrivial examples have as yet appeared in physical theories. These fields appear well suited for describing broken symmetries either in conjunction with or instead of the Yang-Mills equations. The harmonic mapping equation is quite similar in many respects to the Einstein equations for gravitation, although simpler in structure, and can describe any gauge symmetry group $G$ broken to a subgroup $H$ in a sense parallel to the way the gravitational (metric) field breaks general covariance [local $\mathrm{GL}(4, R)$ invariance] down to local Lorentz invariance. This paper outlines the basis for a program of exploring harmonic mapping theories to see whether they may provide models of physical phenomena that either are not recognized, or are not well fitted to more familiar field theories.
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Citations
Cites
Quantum Theory of Gravity. II. The Manifestly Covariant Theory
DeWitt, B. S. (1967) · Physical Review · doi:10.1103/physrev.162.1195 · Cited by 1,765
Cited by
Proof of uniqueness of the Kerr-Newman black hole solution
Mazur, P. O. (1982) · Journal of Physics A: Mathematical and General · doi:10.1088/0305-4470/15/10/021 · Cited by 342
Metadata
- Authors
- Misner, C. W.
- Venue
- Physical Review D
- Publisher
- American Physical Society (APS)
- Published
- 1978-12-15
- Volume
- 18
- Issue
- 12
- Pages
- 4510-4524
- ISSN
- 0556-2821 (ISSN-L)
- OpenAlex
- W2103376451
- Cited by
- 164
- References
- 1
- FWCI
- 8.19
- Type
- journal article
- Language
- en
- Open access
- closed
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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