Nonlinear chiral models and many-dimensional solitons

K. J. Barnes; I. J. Ketley; D. A. Nicole; P. J. O'Donnell

doi:10.1103/PhysRevD.16.511

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Nonlinear chiral models and many-dimensional solitons

K. J. Barnes, I. J. Ketley^*, D. A. Nicole, and P. J. O'Donnell^†

Department of Physics, University of Southampton, Southampton, England

^*Department of Mathematics.
^†Work supported in part by the Science Research Council. Permanent address: Department of Physics and Scarborough College, University of Toronto, Toronto, Canada M5S 1A1.

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Phys. Rev. D 16, 511 – Published 15 July, 1977

DOI: https://doi.org/10.1103/PhysRevD.16.511

Abstract

The problem of obtaining exact, finite-energy, static solutions to the equations of motion of nonlinear chiral SU(2) x SU(2) Lagrangians is investigated in a framework which is independent of the coordinate system for the pion fields. This approach considerably simplifies the derivation of the equations and exhibits clearly the topological nature of the solutions where these are known. Two promising unsolved models are considered and shown to contain (in appropriate limits) previously considered models for which properties of the static solutions have been established.

References (11)

R. Rajaraman, Phys. Rep. 21C, 227 (1975) S. Coleman, lecture notes, International School of Subnuclear Physics, "Ettore Majorana," 1975 (unpublished)
R. Hobart, Proc. Phys. Soc. London A82, 201 (1963) G. H. Derrick, J. Math. Phys. 5, 1252 (1964) G. Rosen, ibid. 7, 2066 (1966)
M. J. Duff and C. J. Isham, Nucl. Phys. B108, 130 (1976) S. Deser, M. J. Duff, and C. J. Isham, ibid. B111, 45 (1976)
L. D. Faddeev, CERN Report No. CERN TH. 2188, 1976 (unpublished)
J. Hietarinta, J. Math. Phys. 18, 65 (1977) J. Honerkamp et al., Lett. Nuovo Cimento 15, 97 (1976)
K. J. Barnes, P. H. Dondi, and S. C. Sarkar, Proc. R. Soc. London A330, 389 (1972) K. J. Barnes and C. J. Isham, Nucl. Phys. B15, 333 (1970)
P. Chang and F. Gürsey, Phys. Rev. 164, 1752 (1967)
F. G. Tricomi, Differential Equations (Hafner, New York, 1961)
T. H. R. Skyrme, Proc. R. Soc. London A260, 127 (1961)
T. T. Wu and C. N. Yang, in Properties of Matter under Unusual Conditions, edited by H. Mark and S. Fernbach (Interscience, New York, 1969), p. 349 G. 't Hooft, Nucl. Phys. B79, 276 (1974) B. Julia and A. Zee, Phys. Rev. D 11, 2227 (1975)
M. K. Prasad and C. M. Sommerfield, Phys. Rev. Lett. 35, 760 (1975)

[c1] R. Rajaraman, Phys. Rep. 21C, 227 (1975) S. Coleman, lecture notes, International School of Subnuclear Physics, "Ettore Majorana," 1975 (unpublished)

[c2] R. Hobart, Proc. Phys. Soc. London A82, 201 (1963) G. H. Derrick, J. Math. Phys. 5, 1252 (1964) G. Rosen, ibid. 7, 2066 (1966)

[c3] M. J. Duff and C. J. Isham, Nucl. Phys. B108, 130 (1976) S. Deser, M. J. Duff, and C. J. Isham, ibid. B111, 45 (1976)

[c4] L. D. Faddeev, CERN Report No. CERN TH. 2188, 1976 (unpublished)

[c5] J. Hietarinta, J. Math. Phys. 18, 65 (1977) J. Honerkamp et al., Lett. Nuovo Cimento 15, 97 (1976)

[c6] K. J. Barnes, P. H. Dondi, and S. C. Sarkar, Proc. R. Soc. London A330, 389 (1972) K. J. Barnes and C. J. Isham, Nucl. Phys. B15, 333 (1970)

[c7] P. Chang and F. Gürsey, Phys. Rev. 164, 1752 (1967)

[c8] F. G. Tricomi, Differential Equations (Hafner, New York, 1961)

[c9] T. H. R. Skyrme, Proc. R. Soc. London A260, 127 (1961)

[c10] T. T. Wu and C. N. Yang, in Properties of Matter under Unusual Conditions, edited by H. Mark and S. Fernbach (Interscience, New York, 1969), p. 349 G. 't Hooft, Nucl. Phys. B79, 276 (1974) B. Julia and A. Zee, Phys. Rev. D 11, 2227 (1975)

[c11] M. K. Prasad and C. M. Sommerfield, Phys. Rev. Lett. 35, 760 (1975)

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Nonlinear chiral models and many-dimensional solitons

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