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Aspects of Skyrmions

Aspects of Skyrmions. Paul Sutcliffe. University of Kent. Aspects of Skyrmions. Work with Richard Battye, Michael Atiyah, Steffen Krusch, Nick Manton. Skyrmions and the pion mass, Battye & Sutcliffe, Nucl. Phys. B705, 384 (2004). Skyrmions, instantons, mass and curvature ,

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Aspects of Skyrmions

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  1. Aspects of Skyrmions Paul Sutcliffe University of Kent

  2. Aspects of Skyrmions Work with Richard Battye, Michael Atiyah, Steffen Krusch, Nick Manton. Skyrmions and the pion mass, Battye & Sutcliffe, Nucl. Phys. B705, 384 (2004). Skyrmions, instantons, mass and curvature, Atiyah & Sutcliffe, Phys. Lett. B605, 106 (2005). Spinning Skyrmions and the Skyrme parameters, Battye, Krusch & Sutcliffe, hep-th/0507279.

  3. Aspects of Skyrmions • The Skyrme model. • Skyrme parameters from spinning Skyrmions. • Multi-Skyrmions; shells & crystals. • New shapes for multi-Skyrmions. • Alpha particle model & cubes. • Conclusion.

  4. The Skyrme model 3 parameters, Nonlinear pion theory: Topological solitons (Skyrmions); Winding number, B, identified with Baryon number.

  5. Skyrme Parameters Use energy and length units of Rescaled pion mass, Two commonly used values;

  6. Spinning a Skyrmion B=1. Conserved quantities; spin J, and isospin I. Isospin rotation For B=1 Skyrmion, J=I. Adkins, Nappi & Witten (1983); rigid body approximation.

  7. Skyrmions B=1,...,22

  8. A problem with shells.

  9. Skyrmion Energies

  10. B=32 Shell vs. Crystal shell crystal

  11. B=8 with m=2

  12. B=9 with m=2

  13. B=10 with m=2

  14. B=12 with m=2

  15. Alpha particle model --- how to put cubes together? The Skyrmion version of this is configurations formed from B=4 cubes. B=12 Triangular symmetry. Are there 3 cubes here?

  16. Cube - Cube Interactions Colour Skyrmions using pion field direction 900 twist lowers energy same orientation

  17. 3 Cubes in a Triangle: B=12 ? ? 1200 twist, edge in no twist, face in

  18. Conclusions • Skyrme parameters should be changed from the values commonly used. • A large pion mass changes the shapes of multi-Skyrmions. • Symmetric shells are replaced by less symmetric non-spherical structures. • Crystal chunks and cubes may play an important role. • More field simulations currently in progress.

  19. THE END

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