The Yang-Mills equations on the universal cosmos. (English) Zbl 0535.58022

In this paper, the authors extend the earlier results of the third author [ibid. 33, 175-194 (1979; Zbl 0416.58027)] and D. M. Eardley and V. Moncrief [Commun. Math. Phys. 83, 171-191 (1982; Zbl 0496.35061), 193-212 (1982; Zbl 0496.35062)] on the existence of a solution to the Cauchy problem for the Yang-Mills equations (in the temporal gauge) to a model of space-time recently investigated by the second author and the third author [J. Funct. Anal. 47, 78-142 (1982; Zbl 0535.58019)]. It also employs some geometric techniques previously used by the first author and D. Christodoulou [Ann. Sci. Ec. Norm. Supér., IV. Sér. 14, 481-506 (1981; Zbl 0499.35076)]. To show the global existence of solutions of conformally invariant partial differential equations having small Cauchy data. Contents include an introduction; non-linear one-parameter groups; the Yang-Mills equations; solution of the Cauchy problem; relations between solutions on the universal cosmos and on Minkowski space-time; asymptotics of fields; asymptotics of solutions to the Yang-Mills equations on Minkowski space- time.
Reviewer: J.Zund


53D50 Geometric quantization
53C80 Applications of global differential geometry to the sciences
81T08 Constructive quantum field theory
81T20 Quantum field theory on curved space or space-time backgrounds
Full Text: DOI


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