On the positivity preservation of the free Euclidean Dirac equation
Norbert Barankai
TL;DR
This paper investigates the conditions under which the free Euclidean Dirac equation maintains the positivity of initial data, revealing that this property holds exclusively in two-dimensional spacetime.
Contribution
It establishes a dimensional restriction for positivity preservation in the free Euclidean Dirac equation, a novel result in the analysis of relativistic quantum equations.
Findings
Positivity preservation occurs only in two spacetime dimensions.
Higher dimensions do not support positivity preservation for this equation.
The result impacts the understanding of relativistic quantum dynamics.
Abstract
We show that the free Euclidean Dirac equation can preserve the positivity of its initial data only in two spacetime dimensions.
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Taxonomy
TopicsAdvanced Mathematical Physics Problems · advanced mathematical theories · Black Holes and Theoretical Physics