Conserved quantity partition for Dirac's equation

Author:
Thomas P. Branson

Journal:
Quart. Appl. Math. **42** (1984), 179-191

MSC:
Primary 35Q20; Secondary 35L45, 81D25

DOI:
https://doi.org/10.1090/qam/745098

MathSciNet review:
745098

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Abstract: Let be the -dimensional Minkowski space, . The energy of a solution to Dirac's equation in is a sum of terms, the th term depending on and the space derivative . We show that if the Cauchy datum for is compactly supported, then each of these terms is eventually constant. Specifically, if is initially supported in the closed ball of radius about the origin in space , then for times , the th term is equal to the energy of the th Riesz transform , which also solves Dirac's equation.

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DOI:
https://doi.org/10.1090/qam/745098

Article copyright:
© Copyright 1984
American Mathematical Society