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All Journal JOURNAL OF NATURAL SCIENCES AND MATHEMATICS RESEARCH Journal of Natural Sciences and Mathematics Research
Muhammad Ardhi Khalif, Muhammad Ardhi
Department of Physics, FITK Universitas Islam Negeri Walisongo, Semarang, Central Java
Agriculture, Biological Sciences & Forestry Biochemistry, Genetics & Molecular Biology Chemistry Materials Science & Nanotechnology Mathematics Physics

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Quaternionic Version of Rotation Groups and Lorentz Group Rahmawati, Latief; Khalif, Muhammad Ardhi; Rosyid, Muhammad Farchani
JOURNAL OF NATURAL SCIENCES AND MATHEMATICS RESEARCH 2015: JNSMR Volume 1 Issue 1 Year 2015
Publisher : Fakultas Ilmu Tarbiyah dan Keguruan, UIN Walisongo

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Abstract

Quaternionic version of rotation groups and Lorentz Group has been constructed. The rotation groups that has been discussed were quaternionic version of groups , O(3), and SO(3). The Lorentz groups that has been discussed were quaternionic version of groups SL(2;C), O(3; 1), and SOo(3; 1). Starting from the definition of each group, the parameters of the group were obtained. Finally the generators of the group were obtained. The commutation of the generator were also computed. 
Lorentz Group Action on Ellips Space Khalif, Muhammad Ardhi
Journal Of Natural Sciences And Mathematics Research Vol 1, No 2 (2015): Volume 1, Nomor 2, 2015
Publisher : Faculty of Science and Technology, State Islamic University Walisongo Central Java

Show Abstract | Download Original | Original Source | Check in Google Scholar | 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.
Co-Authors Latief Rahmawati, Latief Muhammad Farchani Rosyid