Special Issue "Harmonic Oscillators and Two-by-two Matrices in Modern Physics"

A special issue of Symmetry (ISSN 2073-8994).

Deadline for manuscript submissions: 31 March 2019

Special Issue Editor

Guest Editor
Prof. Dr. Young Suh Kim

Center for Fundamental Physics, University of Maryland, College Park, MD 20742, USA
Website | E-Mail
Interests: elementary particle theory; Lorentz group applicable to other areas of physics including quantum optics; condensed matter physics; and classical mechanics; foundations of quantum mechanics; particularly the question of making the uncertainty principle consistent with special relativity

Special Issue Information

Dear Colleagues,

From a mathematical point of view, modern physics is the physics of harmonic oscillators and two-by-two matrices. The oscillator's role in the development of quantum mechanics is well known. Since then, the harmonic oscillator played the major roles in the formulations of the Fock space in quantum field theory, quantum optics, superconductivity, atomic and molecular physics, among others,

As for two-by-two matrices, the role of the three Pauli matrices is well known. These three Pauli matrices are Hermitian. Often forgotten is the fact that there are also three two-by-two anti-Hermitian matrices. These six matrices constitute the complete set of generators for the most general form of two-by-two matrices with unit determinant. The group of these six-parameter matrices is known as the group SL(2,c).

Indeed, the SL(2,c) group leads to the mathematics of the Lorentz group which Einstein used when he developed his special theory of relativity. While the Hermitian Pauli matrices generate rotations, the three anti-Hermitian matrices lead to squeeze transformations. These squeeze operations are quite common in many branches of physics, including engineering applications, crystal physics, superconductivity, quantum optics, entanglement problems, among others.

It is quite possible that you are using harmonic oscillators and/or two-by-two matrices in the paper you are working on these days. If you feel that these mathematical instruments are useful in understanding the physical problems and in explaining your results to others, you are welcome to submit your paper to this Special Issue.

If you would like to organize the papers you wrote in the past, you are welcome to write a review paper using these two mathematical instruments. It is the aim of this Special Issue to gather works on these topics, which provide a representative overview, as well as to stimulate progress in their investigation.

Prof. Dr. Young Suh Kim
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1200 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.


  • Harmonic oscillators
  • Two-by-two matrices

Published Papers

This special issue is now open for submission.
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