×

zbMATH — the first resource for mathematics

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

MSC:
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
PDF BibTeX XML Cite
Full Text: DOI
References:
[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.