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Extra dimensions in high energy physics: Symmetry and symmetry breaking.

机译:高能物理中的额外维度:对称和对称破坏。

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摘要

Ever since Kaluza's remarkable paper in 1921 where he successfully unified Einstein's General Theory of Relativity with Maxwell's Electromagnetism by invoking an extra “fifth” dimension, extra dimensions, i.e. dimensions other than the regularly observed three dimensions of space and one dimension of time, have played an intriguing but often essential role in high energy physics and cosmology. The fundamental reason behind the success of extra dimensions (either mathematical or physical in nature) lies in its ability to “geometrize” symmetries. Symmetries which are algebraically realized in four dimensional theories can be identified with the space-time symmetries or isometries of the extra dimensions and this has several important benefits. For example, one can understand and implement various symmetry breaking mechanisms using the geometric symmetries of the extra dimensions.; In my dissertation, I consider three different problems exploring and utilizing these deep connections between symmetry, symmetry breaking and extra dimensions. In the first problem we show how one can add a “radial coordinate” to deSitter space-times to get a higher dimensional flat space-time. The process can now be inverted to obtain theories on deSitter space-times from known theories on flat space-times. In the second problem, I discuss Kaluza-Klein theories where our universe is considered to be truly higher dimensional in nature. In particular I explore the possibility of explaining symmetry breaking in gauge theories through a transition of the extra dimensional manifold from a more symmetric to a less symmetric metric space. I also consider cosmological implications of such a phase transition. Finally, the last problem concerns harmonic superspace formalism, where one introduces extra fermionic coordinates and “harmonic coordinates” to geometrize supersymmetry and R-symmetry respectively.
机译:自从1921年卡卢扎发表非凡的论文以来,他通过引用一个额外的“第五”维,成功地将爱因斯坦的相对论和麦克斯韦的电磁学统一起来,额外的维,即除了通常观察到的空间的三个维和一个时间的维之外的维在高能物理和宇宙学中一个有趣但通常必不可少的角色。额外维度(无论是数学上还是物理上的)成功的根本原因在于其“对称化”几何形状的能力。在四维理论中以代数形式实现的对称性可以通过时空对称性或额外维的对称性来识别,这具有许多重要的好处。例如,可以使用额外尺寸的几何对称性来理解和实现各种对称性破坏机制。在我的论文中,我考虑了三个不同的问题,这些问题探索和利用了对称性,对称性破坏和额外维度之间的深层联系。在第一个问题中,我们展示了如何向deSitter时空添加“径向坐标”以获得更高维的平面时空。现在可以颠倒该过程,以从平面时空的已知理论获得关于deSitter时空的理论。在第二个问题中,我讨论了Kaluza-Klein理论,其中我们的宇宙在本质上被认为是真正的高维。特别是,我探索了通过超维流形从一个较对称的度量空间到一个较不对称的度量空间的转换来解释规范理论中对称性破裂的可能性。我还考虑了这种相变的宇宙学意义。最后,最后一个问题涉及调和超空间形式主义,其中引入了额外的费米子坐标和“调和坐标”来分别使几何超对称性和R-对称性。

著录项

  • 作者

    Biswas, Tirthabir.;

  • 作者单位

    State University of New York at Stony Brook.;

  • 授予单位 State University of New York at Stony Brook.;
  • 学科 Physics Elementary Particles and High Energy.
  • 学位 Ph.D.
  • 年度 2003
  • 页码 p.4430
  • 总页数 276
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类 高能物理学;
  • 关键词

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