Special Issue "A Commemorative Issue in Honor of the 120th Anniversary of the Birth of Professor Paul Dirac: Dirac's Forms of Relativistic Quantum Dynamics and Internal Space-Time Symmetries"

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Physics and Symmetry/Asymmetry".

Deadline for manuscript submissions: 30 April 2023 | Viewed by 3902

Special Issue Editors

Prof. Dr. Young S. Kim
E-Mail Website
Guest Editor
Center for Theoretical Physics, University of Maryland, College Park, MD, USA
Interests: physics of the Lorentz group; relativistic quantum mechanics; quantum optics; relativistic harmonic oscillators; internal space-time symmetries; Lorentz covariant quantum mechanics; physical consequences of Einstein’s E=mc2 ; combining the work of Wigner, Dirac, and Feynman
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Marilyn E. Noz
E-Mail
Guest Editor
Department of Radiology, New York University, New York, NY, USA
Interests: relativistic quantum mechanics; Two-by-two matrix representation of group theory; Harmonics oscillators; the Lorentz and Poincaré groups; Wigner’s little groups; Neutrinos and gauge invariance

Special Issue Information

Dear Colleagues,

Paul A. M. Dirac spent his entire working life trying to reconcile quantum mechanics with special relativity. His equation for the electron and positron is a case in point. Indeed, the Dirac equation is the correct language for the electron spin in the Lorentz-covariant world and has application to the present day study of neutrinos. Dirac was also interested in particles with space-time extensions and their internal space-time symmetries. This became the major issue when the proton became a bound state of the quarks. What happens when the proton moves with speed close to that of light? This and many other problems can be investigated according to the suggestions made by Dirac during the period from 1927 to 1963. This special issue can include the papers on the Dirac equation, higher-spin particles in the relativistic world; symmetries of the hydrogen atom and harmonic oscillators; neutrinos both massless and with small mass; standing waves, and string models in the Lorentz-covariant regime.

Prof. Dr. Young S. Kim
Prof. Dr. Marilyn E. Noz
Guest Editors

Manuscript Submission Information

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Keywords

  • Dirac’s Equation
  • Coupled harmonic oscillators
  • Internal space-time symmetries
  • Quantum mechanics of bound states
  • Massless and small-mass neutrinos
  • Special relativity in the quantum world
  • Bound state of quarks
  • Lorentz covariance
  • Quarks versus partons
  • Standing waves

Published Papers (3 papers)

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Research

Article
Chiral Dirac Equation and Its Spacetime and CPT Symmetries
Symmetry 2021, 13(9), 1608; https://doi.org/10.3390/sym13091608 - 02 Sep 2021
Cited by 1 | Viewed by 670
Abstract
The Dirac equation with chiral symmetry is derived using the irreducible representations of the Poincaré group, the Lagrangian formalism, and a novel method of projection operators that takes as its starting point the minimal assumption of four linearly independent physical states. We thereby [...] Read more.
The Dirac equation with chiral symmetry is derived using the irreducible representations of the Poincaré group, the Lagrangian formalism, and a novel method of projection operators that takes as its starting point the minimal assumption of four linearly independent physical states. We thereby demonstrate the fundamental nature of this form of the Dirac equation. The resulting equation is then examined within the context of spacetime and CPT symmetries with a discussion of the implications for the general formulation of physical theories. Full article
Article
Integration of Dirac’s Efforts to Construct a Quantum Mechanics Which is Lorentz-Covariant
Symmetry 2020, 12(8), 1270; https://doi.org/10.3390/sym12081270 - 01 Aug 2020
Cited by 2 | Viewed by 1030
Abstract
The lifelong efforts of Paul A. M. Dirac were to construct localized quantum systems in the Lorentz covariant world. In 1927, he noted that the time-energy uncertainty should be included in the Lorentz-covariant picture. In 1945, he attempted to construct a representation of [...] Read more.
The lifelong efforts of Paul A. M. Dirac were to construct localized quantum systems in the Lorentz covariant world. In 1927, he noted that the time-energy uncertainty should be included in the Lorentz-covariant picture. In 1945, he attempted to construct a representation of the Lorentz group using a normalizable Gaussian function localized both in the space and time variables. In 1949, he introduced his instant form to exclude time-like oscillations. He also introduced the light-cone coordinate system for Lorentz boosts. Also in 1949, he stated the Lie algebra of the inhomogeneous Lorentz group can serve as the uncertainty relations in the Lorentz-covariant world. It is possible to integrate these three papers to produce the harmonic oscillator wave function which can be Lorentz-transformed. In addition, Dirac, in 1963, considered two coupled oscillators to derive the Lie algebra for the generators of the O(3,2) de Sitter group, which has ten generators. It is proven possible to contract this group to the inhomogeneous Lorentz group with ten generators, which constitute the fundamental symmetry of quantum mechanics in Einstein’s Lorentz-covariant world. Full article
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Article
SU(2) × SU(2) Algebras and the Lorentz Group O(3,3)
Symmetry 2020, 12(5), 817; https://doi.org/10.3390/sym12050817 - 15 May 2020
Viewed by 1349
Abstract
The Lie algebra of the Lorentz group O(3,3) admits two types of SU(2) × SU(2) subalgebras: a standard form based on spatial rotation generators and a second form based on temporal rotation generators. The units of measurement for the conserved [...] Read more.
The Lie algebra of the Lorentz group O(3,3) admits two types of SU(2) × SU(2) subalgebras: a standard form based on spatial rotation generators and a second form based on temporal rotation generators. The units of measurement for the conserved quantity due to invariance under temporal rotations are investigated and found to be the same units of measure as the Planck constant. The breaking of time reversal symmetry is considered and found to affect the chiral properties of a temporal SU(2) × SU(2) algebra. Finally, the symmetry between algebras is explored and pairs of algebras are found to be related by SU(2) × U(1) symmetry, while a group of three algebras are related by SO(4) symmetry. Full article
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