Simple fivedimensional wave equation for a Dirac particle
Abstract
A firstorder relativistic wave equation is constructed in five dimensions. Its solutions are eightcomponent spinors, interpreted as singleparticle fermion wave functions in fourdimensional spacetime. Use of a ''cylinder condition'' (the removal of explicit dependence on the fifth coordinate) reduces each eightcomponent solution to a pair of degenerate fourcomponent spinors. It is shown that, when the cylinder condition is applied, the results obtained from the new equation are the same as those obtained from the Dirac equation. Without the cylinder condition, on the other hand, the equation implies the existence of a scalar potential, and for zeromass particles it leads to a fourdimensional fermionic equation analogous to Maxwell's equation with sources.
 Authors:
 Department of Physics, Texas Tech University, MS 1051, Lubbock, Texas 79409 (United States)
 Publication Date:
 OSTI Identifier:
 20929635
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Journal of Mathematical Physics; Journal Volume: 48; Journal Issue: 2; Other Information: DOI: 10.1063/1.2435983; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; COORDINATES; CYLINDERS; DIRAC EQUATION; FERMIONS; FOURDIMENSIONAL CALCULATIONS; MANYDIMENSIONAL CALCULATIONS; MATHEMATICAL SOLUTIONS; MAXWELL EQUATIONS; POTENTIALS; QUANTUM MECHANICS; RELATIVISTIC RANGE; SCALARS; SPACETIME; SPINORS; WAVE FUNCTIONS
Citation Formats
Redington, N., and Lodhi, M. A. K.. Simple fivedimensional wave equation for a Dirac particle. United States: N. p., 2007.
Web. doi:10.1063/1.2435983.
Redington, N., & Lodhi, M. A. K.. Simple fivedimensional wave equation for a Dirac particle. United States. doi:10.1063/1.2435983.
Redington, N., and Lodhi, M. A. K.. Thu .
"Simple fivedimensional wave equation for a Dirac particle". United States.
doi:10.1063/1.2435983.
@article{osti_20929635,
title = {Simple fivedimensional wave equation for a Dirac particle},
author = {Redington, N. and Lodhi, M. A. K.},
abstractNote = {A firstorder relativistic wave equation is constructed in five dimensions. Its solutions are eightcomponent spinors, interpreted as singleparticle fermion wave functions in fourdimensional spacetime. Use of a ''cylinder condition'' (the removal of explicit dependence on the fifth coordinate) reduces each eightcomponent solution to a pair of degenerate fourcomponent spinors. It is shown that, when the cylinder condition is applied, the results obtained from the new equation are the same as those obtained from the Dirac equation. Without the cylinder condition, on the other hand, the equation implies the existence of a scalar potential, and for zeromass particles it leads to a fourdimensional fermionic equation analogous to Maxwell's equation with sources.},
doi = {10.1063/1.2435983},
journal = {Journal of Mathematical Physics},
number = 2,
volume = 48,
place = {United States},
year = {Thu Feb 15 00:00:00 EST 2007},
month = {Thu Feb 15 00:00:00 EST 2007}
}

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