zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
The existence of Chern-Simons vortices. (English) Zbl 0733.58009
The paper deals with a new type of vortices, called Chern-Simons vortices, suggested recently by Jackiw and Weinberg as well as by Hong, Kim and Pac in the problem of charged vortices with gauge field governed by the Chern-Simons terms of the action. The author establishes the existence theorem for these vortices. The main part of the paper is the investigation of analytical and variational problems raised from the Chern-Simons equation.

58D30Spaces and manifolds of mappings in applications to physics
81V10Electromagnetic interaction; quantum electrodynamics
Full Text: DOI
[1] Aubin, T.: Nonlinear analysis on manifolds. Monge-Ampere equations. Berlin, Heidelberg, New York: Springer 1982 · Zbl 0512.53044
[2] Bradlow, S.: Vortices on Kähler manifolds. Thesis, University of Chicago, 1988
[3] Deser, S., Jackiw, R., Templeton, S.: Topological massive gauge theories. Ann. Phys.140, 372--411 (1982) · doi:10.1016/0003-4916(82)90164-6
[4] Chen, Y.Y.: Vortices for the Ginzburg-Landau equations--the nonsymmetric case in bounded domain. AMS Contemporary Mathematics, Number 108, 1990 · Zbl 0705.35113
[5] Evans, L.C.: Weak convergence method for nonlinear partial differential equations. AMS Regional Conference Series in Mathematics, Number 74
[6] Fröhlich, J., Marchetti, P.A.: Quantum field theories of vortices and anyons. Commun. Math. Phys.121, 177--223 (1989) · Zbl 0819.58045 · doi:10.1007/BF01217803
[7] Gilbarg, D., Trudinger, N.: Elliptic partial differential equations of second order. Second Ed. Berlin, Heidelberg, New York: Springer 1983 · Zbl 0562.35001
[8] Ginzburg, V. L., Landau, L.D.: On the theory of superconductivity. Zh. Eksper. Theoret. Fiz.20, 1064--1073 (1950)
[9] Hagen, C.R.:A new gauge theory without an elementary Photon. Ann. Phys.157, 342--359 (1984) · doi:10.1016/0003-4916(84)90064-2
[10] Jackiw, R., Weinberg, E.J.: Self-dual Chern-Simons vortices. Preprint submitted to Phys. Lett., Feb. 1990 · Zbl 1050.81595
[11] Jackiw, R., Pi, S.-Y.: Gauged nonlinear Schrödinger equation on the plane. Preprint submitted to Phys. Lett., June 1990 · Zbl 1050.81526
[12] Jackiw, R., Pi, S.-Y.: Classical and quantal nonrelativistic Chern-Simons theory. Preprint submitted to Phys. Rev. D15, June 1990
[13] Morry, C.B., Jr.: Multiple integrals in the calculus of variations. Berlin, Heidelberg, New York: Springer 1966
[14] Jaffe, A., Taubes, C.: Vortices and monopoles. Boston: Birkhäuser 1980 · Zbl 0457.53034
[15] Taubes, C.: Arbitraryn-vortex solutions to the first order Ginzburg-Landau equations. Commun. Math. Phys.72, 277--292 (1980) · Zbl 0451.35101 · doi:10.1007/BF01197552
[16] Schiff, J.: Integrability of Chern-Simons-Higgs and abelian Higgs equations in a background metric. Preprint submitted to Phys. Lett., March 1990 · Zbl 0743.35057
[17] Smoller, J., Yau, S.-T.: To appear in the collected volumes on UCLA Summer School in Geometry, 1990
[18] Hong, J., Kim, Y., Pac, P.Y.: Phys. Rev. Lett.64, 2230 (1990) · Zbl 1014.58500 · doi:10.1103/PhysRevLett.64.2230