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Muhammad Ardhi Khalif
Department of Physics, Faculty of Science and Technology, Semarang
Agriculture, Biological Sciences & Forestry Biochemistry, Genetics & Molecular Biology Chemistry Materials Science & Nanotechnology Physics

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Lorentz Group Action on Ellips Space Muhammad Ardhi Khalif
Journal of Natural Sciences and Mathematics Research Vol 1, No 2 (2015): December
Publisher : Faculty of Science and Technology, Universitas Islam Negeri Walisongo Semarang

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (308.267 KB) | DOI: 10.21580/jnsmr.2015.1.2.1602

Abstract

The ellips space E has been constructed as cartesian product R+ × R+ × [ π 2 , π 2 ]. Its elements, (a, b, θ), is called as an ellipse with eccentricity is = p1 − b2/a2 if b a and is = p1 − a2/b2 if a b. The points (a, b, π/2) is equal to (b, a, 0). The action of subgrup SOoz(3, 1) of Lorentz group SOo(3, 1), containing Lorentz transformations on x−y plane and rotations about z axes, on E is defined as Lorentz transformation or rotation transformation of points in an ellipse. The action is effective since there are no rigid points in E. The action is also not free and transitive. These properties means that Lorentz transformations change any ellips into another ellips. Although mathematically we can move from an ellipse to another one with the bigger eccentrity but it is imposible physically. This is occured because we donot include the speed parameter into the definition of an ellipse in E.
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