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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
[1] Segal, I.E, J. funct. anal., 33, 175-194, (1979)
[2] Choquet-Bruhat, Y; Christodoulou, D, Ann. ecole norm. sup. ser. 4, 14, 481-500, (1981)
[3] Christodoulou, D, C. R. acad. sci. (Paris), 293, 139, (1981)
[4] Eardley, D; Moncrief, V; Eardley, D; Moncrief, V, Comm. math. phys., Comm. math. phys., 83, 193-212, (1982)
[5] Choquet-Bruhat, Y; Segal, I.E, C. R. acad. sci. (Paris), 294, 225-230, (1982)
[6] Segal, I.E, Mathematical cosmology and extragalactic astronomy, (1976), Academic Press New York
[7] Paneitz, S.M; Segal, I.E, J. funct. anal., 47, 78-142, (1982)
[8] Glassey, R.T; Strass, W.A, Comm. math. phys., 65, 1-13, (1979)
[9] Glassey, R.T; Strauss, W.A, Comm. math. phys., 67, 51-67, (1979)
[10] Leray, J, Hyperbolic differential equations, (1952), Institute for Advanced Study Princeton, NJ
[11] Ginibre, J; Velo, G, Comm. math. phys., 82, 1-28, (1981)
[12] Ginibre, J; Velo, G, Ann. inst. H. Poincaré, 36, 59-78, (1982)
[13] Kerner, R, Ann. inst. H. Poincaré, 20, 279-283, (1974)
[14] Choquet-Bruhat, Y, ()
[15] Glassey, R.T; Strauss, W.A, Comm. math. phys., 81, 171-187, (1981)
[16] \scY. Choquet-Bruhat, Lectures on global solutions of hyperbolic equations of gauge theories, Fourth Silarg Symposium, organized by C. Aragone, University Simon Bolivar, Caracas, Venezuela.
[17] Segal, I.E, Ann. of math., 78, 339-364, (1963), (2)
[18] Goodman, R, J. funct. anal., 6, 218-236, (1969)
[19] Lichnerowicz, A, Global theory of connections and holonomy groups, (1976), Noordhoff Gronengen
[20] Choquet-Bruhat, Y; Dewitt-Morette, C, Analysis, manifolds, and physics, (1982), North-Holland Amsterdam · Zbl 0492.58001
[21] Chonstrőm, C, Phys. lett., 90B, 267-269, (1980)
[22] Segal, I.E, (), 13-15
[23] Paneitz, S.M; Segal, I.E, J. funct. anal., 49, 335-414, (1982)
[24] Segal, I.E; Jakobsen, H.P; Ørsted, B; Paneitz, S.M; Speh, B, (), 5261-5265
[25] Faddeev, L.D; Slavnov, A.A, Gauge fields: introduction to quantum theory, (1980), Benjamin/Cummings · Zbl 0486.53052
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