Semiclassical Skyrmion equation of motion

The Skyrme Model

“…Some limitations and shortcomings of such an approach were already listed in Section 7.3 and discussed in (Blaizot and Ripka, 1988;Li, Liu and Zhang, 1987;Wambach, Wyld and Sommermann, 1987). Some limitations and shortcomings of such an approach were already listed in Section 7.3 and discussed in (Blaizot and Ripka, 1988;Li, Liu and Zhang, 1987;Wambach, Wyld and Sommermann, 1987).…”

Relativistic collective coordinate quantization of solitons: Spinning Skyrmion

“…(A3) and (A4)]. Therefore, (A, B, C) are determined by three inhomogeneous linear differential equations of second order, EQ i = 0 (i = 1, 2, 3), or another independent set EQ 2 = EQ 3 = EQ Y = 0 with EQ Y given by (8). The boundary conditions for (A, B, C) at r = 0 and r = ∞ are chosen to be the least singular ones among those allowed by the differential equations; (A, B, C) ∼ (1, 1/r 2 , 1/r 2 ) as r → 0 and (A, B, C − A) ∼ (1/r, 1/r 3 , 1/r 2 ) as r → ∞, both up to numerical coefficients.…”

“…While several authors have discussed the deformation of spinning Skyrmions with various physical pictures (see Refs. [4]- [8] for earlier works), we emphasize that the deformation is naturally induced in our treatment of collective coordinates. Another feature of our treatment of rotational collective coordinate is that we introduce it through coordinate-transformed static solitons with new coordinate depending on the time derivative of the collective coordinate [see Eq.…”

Oblate Skyrmions

“…Using the oblate solution, we can then compute the masses of the nucleons (I = J = 1 2 ) and of the ∆-isobar (I = J = 3 2 ). However, several remarks are in order before we go on.…”

“…When Skyrme first introduced its model a few decades ago [1] to describe baryons as solitons in a non-linear field theory of mesons, the solution proposed was in the spherically symmetric hedgehog ansatz. There are reasons to believe that this solution is not adequate for the rotational states such as the nucleon (I = J = 1 2 ) and the ∆ (I = J = 3 2 ) due to centrifugal forces [2][3][4]. Alternative treatments have been proposed in the past with relative success.…”