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Spectral properties of monopoles and gravitational instantons

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Smedley-WilliamsK_0722_macsSS.pdf (5.491Mb)
Date
2022-07
Author
Smedley-Williams, Kim
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Abstract
Motivated by spectral problems arising in gauge theory and gravity, we develop a rigorous proof of infinitely many bound states for a family of radial Laplacians that have Calogero characteristics at the origin and Coulombic ones at infinity. We first study the spectrum of the operator obtained by linearising the Yang-Mills-Higgs equations around a charge one monopole. We then study two Laplace operators on four-dimensional Riemannian manifolds, namely the Laplace operator on the Atiyah-Hitchin moduli space of centred charge two monopoles and the Laplace operator associated with the Taub-bolt family. We apply our theorem to each operator proving they have infinite discrete spectrums and numerically compute the eigenvalues. We compare results to appropriate analytic approximations for each case.
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http://hdl.handle.net/10399/4658
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©Heriot-Watt University, Edinburgh, Scotland, UK EH14 4AS.

Maintained by the Library
Tel: +44 (0)131 451 3577
Library Email: libhelp@hw.ac.uk
ROS Email: open.access@hw.ac.uk

Scottish registered charity number: SC000278

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  • Policies
  • Privacy & Cookies
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AboutCopyright
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