Interaction of hopfions of charge 1 and 2 from product ansatz

We continue the discussion on the interaction energy of the axially symmetric Hopfions evaluated directly from the product anzsatz. The Hopfions are given by the projection of Skyrme model solutions onto the coset space SU(2)/U(1). Our results show that if the separation between the constituents is not small, the product ansatz can be considered as a good approximation to the general pattern of Hopfions interaction both in repulsive and attractive channel.Comment: 7 pages, 10 figures, submitted to EPL. arXiv admin note: text overlap with arXiv:1401.635

Hopfion canonical quantization

We study the effect of the canonical quantization of the rotational mode of the charge Q=1 and Q=2 spinning Hopfions. The axially-symmetric solutions are constructed numerically, it is shown the quantum corrections to the mass of the configurations are relatively large.Comment: 11 pages, 3 figures, Physics Letters B, in pres

Baby Skyrmions stabilized by canonical quantization

We analyse the effect of the canonical quantization of the rotational mode of the O(3) $\sigma$-model which includes the Skyrme term. Numerical evidence is presented that the quantum correction to the mass of the rotationally-invariant charge $n=1,2$ configurations may stabilize the solution even in the limit of vanishing potential. The corresponding range of values of the parameters is discussed.Comment: 10 pages, 4 figure