Klein's paradox in a four-space formulation of Dirac's equation

Klein's paradox - the prediction by Dirac's equation of the anomalous reflection of electrons from a large potential barrier - has attracted the attention of physicists for several decades. Assessments of its significance vary widely: Some say that it is unimportant, because the problem is...

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Bibliographic Details
Published in:Foundations of physics 1991-06, Vol.21 (6), p.633-647
Main Author: EVANS, A. B
Format: Article
Language:English
Subjects:
662220 - Quantum Electrodynamics- (1992-)
Classical and quantum physics: mechanics and fields
DIFFERENTIAL EQUATIONS
DIRAC EQUATION
ELECTRODYNAMICS
EQUATIONS
Exact sciences and technology
FAILURES
FIELD THEORIES
FUNCTIONS
INTERACTIONS
PAIR PRODUCTION
PARTIAL DIFFERENTIAL EQUATIONS
PARTICLE PRODUCTION
Physics
PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
POTENTIALS
QUANTIZATION
QUANTUM ELECTRODYNAMICS
QUANTUM FIELD THEORY
SECOND QUANTIZATION
WAVE EQUATIONS
WAVE FUNCTIONS
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Summary:Klein's paradox - the prediction by Dirac's equation of the anomalous reflection of electrons from a large potential barrier - has attracted the attention of physicists for several decades. Assessments of its significance vary widely: Some say that it is unimportant, because the problem is resolved by second quantization, but for others it represents a real failure of quantum electrodynamics. Here, a 4-space formulation of Dirac's equation gives results formally identical to those of the usual Klein paradox. However, some extra physical detail can be inferred, and this suggests that the most extreme case involves pair production within the potential barrier.
ISSN:0015-9018
1572-9516
DOI:10.1007/BF00733274