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Title: Quantum structure emerging from the transformation design of the Dirac equation

Abstract

It is shown that a quantum structure can be created by a set of chosen constraint conditions that emerge from the transformation design of the Dirac equation in general relativity. As an explanation, the constraints that cause novel bound states with the quantization rule of a 2D Coulomb system are presented. The discussion in this paper provides a systematic way to look for constraints that generate a required quantization rule. -- Highlights: •We perform the transformation design of space and time for spin-1/2 matter waves. •A quantum rule could naturally emerge as constraints imposed on the Dirac equation itself. •New fermion states share the quantum spectrum of a 2D Coulomb system. •Transformation design uncovers a new exact solvable model. •A quantum spectrum can be created by a geometric structure.

Authors:
Publication Date:
OSTI Identifier:
22314822
Resource Type:
Journal Article
Journal Name:
Annals of Physics (New York)
Additional Journal Information:
Journal Volume: 345; Journal Issue: Complete; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0003-4916
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BOUND STATE; DIRAC EQUATION; FERMIONS; GENERAL RELATIVITY THEORY; GEOMETRY; QUANTIZATION; QUANTUM MECHANICS; SPACE; SPIN; TRANSFORMATIONS

Citation Formats

Lin, De-Hone. Quantum structure emerging from the transformation design of the Dirac equation. United States: N. p., 2014. Web. doi:10.1016/J.AOP.2014.03.008.
Lin, De-Hone. Quantum structure emerging from the transformation design of the Dirac equation. United States. https://doi.org/10.1016/J.AOP.2014.03.008
Lin, De-Hone. 2014. "Quantum structure emerging from the transformation design of the Dirac equation". United States. https://doi.org/10.1016/J.AOP.2014.03.008.
@article{osti_22314822,
title = {Quantum structure emerging from the transformation design of the Dirac equation},
author = {Lin, De-Hone},
abstractNote = {It is shown that a quantum structure can be created by a set of chosen constraint conditions that emerge from the transformation design of the Dirac equation in general relativity. As an explanation, the constraints that cause novel bound states with the quantization rule of a 2D Coulomb system are presented. The discussion in this paper provides a systematic way to look for constraints that generate a required quantization rule. -- Highlights: •We perform the transformation design of space and time for spin-1/2 matter waves. •A quantum rule could naturally emerge as constraints imposed on the Dirac equation itself. •New fermion states share the quantum spectrum of a 2D Coulomb system. •Transformation design uncovers a new exact solvable model. •A quantum spectrum can be created by a geometric structure.},
doi = {10.1016/J.AOP.2014.03.008},
url = {https://www.osti.gov/biblio/22314822}, journal = {Annals of Physics (New York)},
issn = {0003-4916},
number = Complete,
volume = 345,
place = {United States},
year = {Sun Jun 15 00:00:00 EDT 2014},
month = {Sun Jun 15 00:00:00 EDT 2014}
}