Harmonic Oscillators and Two-by-two Matrices in Modern Physics
A special issue of Symmetry (ISSN 2073-8994).
Deadline for manuscript submissions: closed (31 March 2019)
Special Issue Editor
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
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Keywords
- Harmonic oscillators
- Two-by-two matrices
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