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Muhammad Ardhi Khalif
Universitas Islam Negeri Walisongo Semarang
Agriculture, Biological Sciences & Forestry Biochemistry, Genetics & Molecular Biology Chemistry Materials Science & Nanotechnology Physics

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Fermion mass formulation in the Modified Left-Right Symmetry Model Nurul Embun Isnawati; Istikomah Istikomah; Muhammad Ardhi Khalif
Journal of Natural Sciences and Mathematics Research Vol 8, No 2 (2022): December
Publisher : Faculty of Science and Technology, Universitas Islam Negeri Walisongo Semarang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.21580/jnsmr.2022.8.2.13633

Abstract

The Modified Left Right Symmetry Model is an extension of the Standard Model. This model introduces left-handed neutrinos to the right sector and a doublet scalar field to the left sector. This model cannot yet explain the mass generation of fermions and neutrinos. This study is theoretical research using the literature review method. Generating the masses of fermions (quark up-down) and electrons through spontaneous symmetry breaking in Yukawa's Lagrangian term produces a particle mass in the left sector, the same as the calculations in the Standard Model. The masses of fermions (up-down quarks) and electrons for the right sector produced in this study are much more massive than those of fermions (up-down quarks) and the left sector. The neutrino masses produced in this study are by following the Seesaw Mechanism. That is, if one neutrino mass is massive, then the other neutrino masses will be light.©2022 JNSMR UIN Walisongo. All rights reserved.
Complete purely algebraic proof of the homomorphism between SU(2) and SO(3) without concerning their topological properties Muhammad Ardhi Khalif; Nur Farida Amalia
Journal of Natural Sciences and Mathematics Research Vol 8, No 2 (2022): December
Publisher : Faculty of Science and Technology, Universitas Islam Negeri Walisongo Semarang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.21580/jnsmr.2022.8.2.17519

Abstract

The aim of this paper is to provide a complete purely algebraic proof of homo-morphism between SU (2) and SO(3) without concerning the topology of bothgroups. The proof is started by introducing a map ϕ : SU (2) → M L(3, C) de-fined as [ϕ(U )] i j ≡ 12 tr(σ i U σ j U † ). Firstly we proof that the map ϕ satisfies[ϕ(U 1 U 2 )] i j = [ϕ(U 1 )] i k [ϕ(U 2 )] k j , for every U 1 , U 2 ∈ SU (2). The next step is toshow that the collection of ϕ(U ) is having orthogonal property and every ϕ(U ) hasdeterminant of 1. After that, we proof that ϕ(I 2 ) = I 3 . Finally, to make sure thatϕ is indeed a homomorphism, not an isomorphism, we proof that ϕ(−U ) = ϕ(U ),∀U ∈ SU (2).
Co-Authors Istikomah Istikomah Nur Farida Amalia Nurul Embun Isnawati