Abstract
Using a numerical implementation of the ADHMN construction, we compute the fields and energy densities of a charge three monopole with tetrahedral symmetry and a charge four monopole with octahedral symmetry. We then construct a one parameter family of spectral curves and Nahm data which represent charge four monopoles with tetrahedral symmetry, which includes the monopole with octahedral symmetry as a special case. In the moduli space approximation, this family describes a novel kind of four monopole scattering and we use our numerical scheme to construct the energy density at various times during the motion.
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References
Atiyah, M.F. and Hitchin, N.J.: The geometry and dynamics of magnetic monopoles. Princeton, NJ: Princeton University Press, 1988
Hitchin, N.J.: Commun. Math. Phys.83, 579 (1982)
Hitchin, N.J.: Commun. Math. Phys.89, 145 (1983)
Hitchin, N.J., Manton, N.S. and Murray, M.K.: Nonlinearity8, 661 (1995)
Houghton, C.J. and Sutcliffe, P.M.: Nonlinearity9, 385 (1996)
Klein, F.: Lectures on the icosahedron. London: Kegan Paul, 1913
Manton, N.S.: Phys. Lett.110B, 54 (1982)
Nahm, W.: The construction of all self-dual multimonopoles by the ADHM method. In: Monopoles in quantum field theory. eds. N.S. Craigie, P. Goddard and W. Nahm, Singapore: World Scientific, 1982
Stuart, D.: Commun. Math. Phys.166, 149 (1994)
Ward, R.S.: Commun. Math. Phys.79, 317 (1981)
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Communicated by A. Jaffe
Address from September 1995, Institute of Mathematics, University of Kent at Canterbury, Canterbury CT2 7NZ. Email: p.m.sutcliffe@ukc.ac.uk
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Houghton, C.J., Sutcliffe, P.M. Tetrahedral and cubic monopoles. Commun.Math. Phys. 180, 343–361 (1996). https://doi.org/10.1007/BF02099717
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DOI: https://doi.org/10.1007/BF02099717