Cutoff quantization and the Skyrmion

Abstract

The putative classical soliton in the minimal nonlinear u model (no Skyrme term) is known to be unstable to collapse. We note that the imposition of a short-distance cutoff (which is anyway physically reasonable for a nonrenormalizable model) yields a stable classical soliton. We further suggest that this cutoff, carrying as it does some implicit dynamical information, be treated as a quantized dynamical variable. The resulting one-(experimentally fixed) parameter model agrees with experiment roughly as well as the simple a model with the Skyrme term. We interpret this feature as an indication of the robustness of the description of the nucleon as being dominated by a hedgehog-type meson cloud. It is suggested that the same approach might be useful in some other situations where the long-distance description of the physics is more precisely known than is the short-distance description.

Generation of scalar-tensor gravity effects in equilibrium state boson stars

“…6 (i.e., those that start at N p = 0 and end at the cusp labled B 1 ) are stable. They are the only ones composed entirely of negative binding energy states, they contain the flat-space limit, and furthermore, results of a dynamical, numerical analysis demonstrate that they are stable against small perturbations [26]. Fig.…”

Cheshire Cat hadrons

“…The general solution for (I.44) with (I.45) is ψ(x, t) = exp −i[ 1 2 (1 + γ 5 )θ − + 1 2 (1 − γ 5 )θ + ] ψ 0 (x, t) (I. 46) where θ ± = θ(x ± t) and ψ 0 is the solution for θ = 0 (for the MIT bag). The boundary condition is satisfied if…”

“…There is one simple way [46] to avoid the Hobart-Derrick collapse without introducing any further terms in the Lagrangian or any other degrees of freedom, which is interesting and in a way, physically relevant. It is to simulate short-distance physics by "drilling" a hole into the skyrmion or equivalently by taking a nonzero ǫ in the energy functional (II.5).…”

Stable soliton resolution for equivariant wave maps exterior to a ball

“…The exterior model was first introduced in the physics literature in [2], as an easier alternative to the Skyrmion equation. Recently, (1.1) was proposed by Bizon, Chmaj, and Maliborski in [3] as a model to study the problem of relaxation to the ground states given by various equivariant harmonic maps.…”

“…Recently, (1.1) was proposed by Bizon, Chmaj, and Maliborski in [3] as a model to study the problem of relaxation to the ground states given by various equivariant harmonic maps. Both [2,3] Andrew Lawrie III-2 stress the analogy of the stationary equation with that of the damped pendulum by demonstrating the existence and uniqueness of the ground state harmonic maps via a phase-plane analysis. The numerical simulations in [3] indicate that for each equivariance class ≥ 1, and each topological class n ≥ 0, every solution scatters to the unique harmonic map Q ,n that lies in E ,n , giving evidence that the soliton resolution conjecture holds true in this exterior model.…”