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Article

Integration of Dirac’s Efforts to Construct a Quantum Mechanics Which is Lorentz-Covariant

by 1,*,† and 2,†
1
Center for Fundamental Physics, University of Maryland, College Park, MD 20742, USA
2
Department of Radiology, New York University, New York, NY 10016, USA
*
Author to whom correspondence should be addressed.
Both authors contributed equally to this work.
Symmetry 2020, 12(8), 1270; https://doi.org/10.3390/sym12081270
Received: 24 June 2020 / Revised: 16 July 2020 / Accepted: 29 July 2020 / Published: 1 August 2020
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. View Full-Text
Keywords: Dirac’s relativistic quantum mechanics; Lorentz-covariant harmonic oscillators; special relativity from the Heisenberg brackets Dirac’s relativistic quantum mechanics; Lorentz-covariant harmonic oscillators; special relativity from the Heisenberg brackets
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MDPI and ACS Style

Kim, Y.S.; Noz, M.E. Integration of Dirac’s Efforts to Construct a Quantum Mechanics Which is Lorentz-Covariant. Symmetry 2020, 12, 1270. https://doi.org/10.3390/sym12081270

AMA Style

Kim YS, Noz ME. 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

Chicago/Turabian Style

Kim, Young S., and Marilyn E. Noz 2020. "Integration of Dirac’s Efforts to Construct a Quantum Mechanics Which is Lorentz-Covariant" Symmetry 12, no. 8: 1270. https://doi.org/10.3390/sym12081270

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