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Quantized Skyrmions with baryon numbers $B=1,2$ and 4 are considered and angularly localized wavefunctions for them are found. By combining a few low angular momentum states, one can construct a quantum state whose spatial density is close to that of the classical Skyrmion, and has the same symmetries. For the B=1 case we find the best localized wavefunction among linear combinations of $j=1/2$ and $j=3/2$ angular momentum states. For B=2, we find that the $j=1$ ground state has toroidal symmetry and a somewhat reduced localization compared to the classical solution. For B=4, where the classical Skyrmion has cubic symmetry, we construct cubically symmetric quantum states by combining the $j=0$ ground state with the lowest rotationally excited $j=4$ state. We use the rational map approximation to compare the classical and quantum baryon densities in the B=2 and B=4 cases.
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We study angularly excited as well as interacting non-topological solitons, so-called Q-balls and their gravitating counterparts, so-called boson stars in 3+1 dimensions. Q-balls and boson stars carry a non-vanishing Noether charge and arise as solutions of complex scalar field models in a flat space-time background and coupled minimally to gravity, respectively. We present examples of interacting Q-balls that arise due to angular excitations, which are closely related to the spherical harmonics. We also construct explicit examples of rotating boson stars that interact with non-rotating boson stars. We observe that rotating boson stars tend to absorb the non-rotating ones for increasing, but reasonably small gravitational coupling. This is a new phenomenon as compared to the flat space-time limit and is related to the negative contribution of the rotation term to the energy density of the solutions. In addition, our results indicate that a system of a rotating and non-rotating boson star can become unstable if the direct interaction term in the potential is large enough. This instability is related to the appearance of ergoregions.
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