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Symmetry
Volume 17
Issue 3
10.3390/sym17030450
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Article

Algebraic and Spectral Analysis of a Novel Hermitian Spin Basis

by
Timothy Ganesan
1,*,
Zeeshan Yousaf
2 and
M. Z. Bhatti
2
1
Department of Physics & Astronomy, University of Calgary, Calgary, AB T2N 1N4, Canada
2
Department of Mathematics, University of the Punjab, Lahore 54590, Pakistan
*
Author to whom correspondence should be addressed.
Symmetry 2025, 17(3), 450; https://doi.org/10.3390/sym17030450
Submission received: 6 January 2025 / Revised: 3 March 2025 / Accepted: 14 March 2025 / Published: 17 March 2025
(This article belongs to the Section B: Mathematics)
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Abstract

This work aims to explore the algebraic and spectral properties of a novel parametric Hermitian non-Pauli spin basis. The primary motivation for this work is to introduce an alternative to the Pauli spin basis for investigating systems where conventional quantum statistics no longer apply. This study explores the symmetries, commutation relations, Lie algebra structures, and ladder operators of the proposed spin matrices. Additionally, it provides discussions on key findings, potential applications, and concludes with some final remarks. An example for modeling the spectrum of a quantum system is provided.
Keywords: non-Pauli spin matrices; Lie algebra; ladder operators; commutation relations; spectral model non-Pauli spin matrices; Lie algebra; ladder operators; commutation relations; spectral model

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MDPI and ACS Style

Ganesan, T.; Yousaf, Z.; Bhatti, M.Z. Algebraic and Spectral Analysis of a Novel Hermitian Spin Basis. Symmetry 2025, 17, 450. https://doi.org/10.3390/sym17030450

AMA Style

Ganesan T, Yousaf Z, Bhatti MZ. Algebraic and Spectral Analysis of a Novel Hermitian Spin Basis. Symmetry. 2025; 17(3):450. https://doi.org/10.3390/sym17030450

Chicago/Turabian Style

Ganesan, Timothy, Zeeshan Yousaf, and M. Z. Bhatti. 2025. "Algebraic and Spectral Analysis of a Novel Hermitian Spin Basis" Symmetry 17, no. 3: 450. https://doi.org/10.3390/sym17030450

APA Style

Ganesan, T., Yousaf, Z., & Bhatti, M. Z. (2025). Algebraic and Spectral Analysis of a Novel Hermitian Spin Basis. Symmetry, 17(3), 450. https://doi.org/10.3390/sym17030450

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