AIMS Mathematics, 2016, 1(1): 1-8. doi: 10.3934/Math.2016.1.1.

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Harmonic Maps Surfaces and Relativistic Strings

Department of Mathematics, University of Texas, Edinbrug, TX, 78540-2999, USA

The harmonic map is introduced and several physical applications are presented. The classical nonlinear σ model can be looked at as the embedding of a two-dimensional surface in a threedimensional sphere, which is itself embedded in a four-dimensional space. A system of nonlinear evolution equations are obtained by working out the zero curvature condition for the Gauss equations relevant to this geometric formulation.
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Keywords harmonic map; curvature; surface; soliton; sigma models

Citation: Paul Bracken. Harmonic Maps Surfaces and Relativistic Strings. AIMS Mathematics, 2016, 1(1): 1-8. doi: 10.3934/Math.2016.1.1

References

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  • 6. C. W. Misner, Harmonic maps as models for physical theories, Phys. Rev. D, 18 (1978), 4510-4524.
  • 7. K. Pohlmeyer, Integrable Hamiltonian Systems and Interactions through Quadratic Constraints, Commun. Math. Phys. 46 (1976), 207-221.

 

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Copyright Info: 2016, Paul Bracken, licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

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