Bounded scalar fields to the surface of a sphere

Document Type : Research Paper

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Abstract

The study of scalar field theory on a surface is an important research area in theoretical physics which can be followed by a different approach. The obtained result by employing a different approach is comparable with the result from a general method. We show that there are similarities between the free fields on a given surface and weak gravitational-interaction fields defined on a Minkowski spacetime. This work is written based on the stereographic projection and Higgs’s method. We find the metric of tangential space based on the Higgs’s approach. We also distinguish between the internal and external surfaces of a sphere with the positive and negative curvature. The result of this paper is to show that there are no same theories from the constraining of the scalar fields to the surfaces with positive or negative curvature. In this paper, the effect of the gravitational background interacting with matter fields is imposed at least up to the first order of the Riemann curvature tensor.

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References

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History

  • Receive Date: 29 January 2017
  • Revise Date: 28 October 2018
  • Accept Date: 03 October 2018

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