×

zbMATH — the first resource for mathematics

The existence of a non-minimal solution to the SU(2) Yang-Mills-Higgs equations on \(R^ 3.\) I. (English) Zbl 0514.58016

MSC:
53D50 Geometric quantization
81T08 Constructive quantum field theory
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Bourguignon, J.P., Lawson, B., Simons, J.: Stability and gap phenomena for Yang-Mills fields. Proc. Natl. Acad. Sci. USA76, 1550 (1979) · Zbl 0408.53023 · doi:10.1073/pnas.76.4.1550
[2] Jaffe, A., Taubes, C.H.: Vortices and Monopoles. Boston: Birkhäuser 1980 · Zbl 0457.53034
[3] Taubes, C. H.: On the equivalence of first and second order equations for gauge theories. Commun. Math. Phys.75, 207 (1980) · Zbl 0448.58029 · doi:10.1007/BF01212709
[4] Atiyah, M. F., Jones, J.D.S.: Topological aspects of Yang-Mills theory. Commun. Math. Phys.61, 97 (1978) · Zbl 0387.55009 · doi:10.1007/BF01609489
[5] Singer, I. M.: Some remarks on the Gribov ambiguity. Commun. Math. Phys.60, 7 (1978) · Zbl 0379.53009 · doi:10.1007/BF01609471
[6] Atiyah, M. F., Bott, R.: On the Yang-Mills equations over Riemann surfaces (to appear) · Zbl 0509.14014
[7] Burzlaff, J.: A finite energy SU (3) solution which does not satisfy the Bogomol’nyi equations. Acta. Phys. Austr. Suppl. (1981)
[8] Maison, D.: Uniqueness of the Prasad-Sommerfield monopole solution. Nucl. Phys.B182, 114 (1981)
[9] Ljusternik, L.: Topology of the calculus of Variations in the large. (Amer. Math. Soc. Transl.16) Providence, R. I.: Amer. Math. Soc. (1966)
[10] Berger, M.: Nonlinearity and functional analysis. New York: Academic Press 1977. See also Palais, R.S.: Ljusternik-?nirelman theory on Banach manifolds. Topology5, 115 (1966)
[11] Uhlenbeck, K.: Connections withL p bounds on curvature. Commun. Math. Phys.83, 31 (1981) · Zbl 0499.58019 · doi:10.1007/BF01947069
[12] Sachs, J., Uhlenbeck, K.: The Existence of minimal 2-spheres. Ann. Math.113, 1 (1981) · Zbl 0462.58014 · doi:10.2307/1971131
[13] Schoen, R., Uhlenbeck, K.: Regularity of minimizing harmonic maps (to appear) · Zbl 0555.58011
[14] Carrigan, R.A., Jr., Trower, W.P.: Superheavy magnetic monopoles. Sci. Am.246, 106 (1982)
[15] Hirsh, M.W.: Differential topology. Berlin, Heidelberg, New York: Springer 1976
[16] Adams, R.A.: Sobolev spaces. New York: Academic Press 1975 · Zbl 0314.46030
[17] Bogomol’nyi, E.B.: The stability of classical solutions. Sov. J. Nucl. Phys.24, 449 (1976)
[18] Prasad, M., Sommerfield, C.: Exact classical solution for the ’t Hooft monopole and the Julia-Zee dyon. Phys. Rev. Lett.35, 760 (1975) · doi:10.1103/PhysRevLett.35.760
[19] Ward, R.: A Yang-Mills Higgs monopole of charge 2. Commun. Math. Phys.79, 317 (1981) · doi:10.1007/BF01208497
[20] Prasad, M.: Yang-Mills Higgs monopole solutions of arbitrary topological charge. Commun. Math. Phys.80, 137 (1981) · doi:10.1007/BF01213599
[21] Hitchin, N.: Monopoles and geodesics. Commun. Math. Phys.83, 579 (1982) · Zbl 0502.58017 · doi:10.1007/BF01208717
[22] Corrigan, E., Goddard, P.: Ann-monopole solution with 4n-1 degrees of freedom. Commun. Math. Phys.80, 575 (1981) · doi:10.1007/BF01941665
[23] Palais, R.: Foundations of global analysis, New York: W.A. Benjamin Co. 1968 · Zbl 0164.11102
[24] Taubes, C.H.: Self-dual Yang-Mills fields on non-self-dual 4-manifolds. J. Diff. Geom.17, 139 (1982) · Zbl 0484.53026
[25] Spanier, E.H.: Algebraic topology. New York: McGraw-Hill, 1966. See also Steenrod, N.: Topology of fibre bundles. Princeton, NJ: Princeton University Press 1951
[26] Goddard, P., Nuyts, J., Olive, D.: Gauge theories and magnetic charge. Nucl. Phys.B125, 1 (1977) · doi:10.1016/0550-3213(77)90221-8
[27] Taubes, C.H.: Surface integrals and monopole charges in non-abelian gauge theories. Commun. Math. Phys.81, 299 (1981) · Zbl 0486.55009 · doi:10.1007/BF01209069
[28] Uhlenbeck, K.: Removable singularities in Yang-Mills fields. Commun. Math. Phys.83, 11 (1982) · Zbl 0491.58032 · doi:10.1007/BF01947068
[29] Weinberg, E.: Parameter counting for multimonopole solutions. Phys. Rev.D20, 936 (1979)
[30] Taubes, C.H.: In preparation
[31] Parker, T., Taubes, C.H.: On Witten’s proof of the positive energy theorem. Commun. Math. Phys.84, 224 (1982) · Zbl 0528.58040 · doi:10.1007/BF01208569
[32] Vainberg, M.M.: Variational methods and method of monotone operators in the theory of nonlinear equations. New York: Wiley 1973 · Zbl 0279.47022
[33] Morrey, C.B.: Multiple integrals in the calculus of variations. Berlin, Heidelberg, New York: Springer 1966 · Zbl 0142.38701
[34] Sedlacek, S.: A direct method for minimizing the Yang-Mills functional over 4-manifolds. Commun. Math. Phys. (to appear) · Zbl 0506.53016
[35] Parker, T.: Gauge theories on 4-dimensional, Riemannian manifolds. Commun. Math. Phys.85, 563-602 (1982) · Zbl 0502.53022 · doi:10.1007/BF01403505
[36] Ladyzhenskaya, O.A.: The mathematical theory of viscous, incompressible flow. London: Gordon and Breach 1963 · Zbl 0121.42701
[37] Vick, J.W.: Homology theory. New York: Academic Press 1973 · Zbl 0262.55005
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.