Scattering for the Yang-Mills equations

Author:
John C. Baez

Journal:
Trans. Amer. Math. Soc. **315** (1989), 823-832

MSC:
Primary 58G30; Secondary 35P25, 47F05, 58G25, 81E13

DOI:
https://doi.org/10.1090/S0002-9947-1989-0949897-7

MathSciNet review:
949897

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Abstract: We construct wave and scattering operators for the Yang-Mills equations on Minkowski space, . Sufficiently regular solutions of the Yang-Mills equations on are known to extend uniquely to solutions of the corresponding equations on the universal cover of its conformal compactification, . Moreover, the boundary of as embedded in is the union of "lightcones at future and past infinity", . We construct wave operators as continuous maps from a space of time-zero Cauchy data for the Yang-Mills equations to Hilbert spaces of Goursat data on . The scattering operator is then a homeomorphism such that , where is the linear isomorphism arising from a conformal transformation of mapping onto . The maps and are shown to be smooth in a certain sense.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1989-0949897-7

Article copyright:
© Copyright 1989
American Mathematical Society