Nonexistence of Skyrmion-Skyrmion and Skyrmion-anti-Skyrmion static equilibria

Journal Article · Sat Jan 15 00:00:00 EST 2011 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.3523469· OSTI ID:21501246

Gibbons, G W ^[1]; Warnick, C M ^[1]; Wong, W W ^[2]

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1. D.A.M.T.P., University of Cambridge, Wilberforce Road, Cambridge CB3 0WA (United Kingdom)
2. D.P.M.M.S., University of Cambridge, Wilberforce Road, Cambridge CB3 0WB (United Kingdom)

We consider classical static Skyrmion-anti-Skyrmion and Skyrmion-Skyrmion configurations, symmetric with respect to a reflection plane, or symmetric up to a G-parity transformation, respectively. We show that the stress tensor component completely normal to the reflection plane, and hence its integral over the plane, is negative definite or positive definite, respectively. Classical Skyrmions always repel classical Skyrmions and classical Skyrmions always attract classical anti-Skyrmions and thus no static equilibrium, whether stable or unstable, is possible in either case. No other symmetry assumption is made and so our results also apply to multi-Skyrmion configurations. Our results are consistent with existing analyses of Skyrmion forces at large separation, and with numerical results on Skymion-anti-Skyrmion configurations in the literature which admit a different reflection symmetry. They also hold for the massive Skyrme model. We also point out that reflection symmetric self-gravitating Skyrmions or black holes with Skyrmion hair cannot rest in symmetric equilibrium with self-gravitating anti-Skyrmions.

• OSTI ID: 21501246
• Journal Information: Journal of Mathematical Physics, Vol. 52, Issue 1; Other Information: DOI: 10.1063/1.3523469; (c) 2011 American Institute of Physics; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BLACK HOLES
DIRAC EQUATION
EQUILIBRIUM
G PARITY
INTEGRALS
SKYRME POTENTIAL
SOLITONS
SYMMETRY
TENSORS
DIFFERENTIAL EQUATIONS
EQUATIONS
FIELD EQUATIONS
NUCLEON-NUCLEON POTENTIAL
PARTIAL DIFFERENTIAL EQUATIONS
PARTICLE PROPERTIES
POTENTIALS
QUASI PARTICLES
WAVE EQUATIONS