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

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

The Quantum Skyrmion in Representations of General Dimension

The representations of general dimension are constructed for the $SU(2)$ Skyrme model, treated quantum mechanically {\it ab initio. } This quantum Skyrme model has a negative mass term correction, that is not present in the classical Hamiltonian. The magnitude of the quantum mechanical mass correction increases with the dimension of the representation of the $SU(2)$ group. In the case of a 5-dimensional representation it is possible to obtain satisfactory predictions for the nucleon mass with the empirical value for the pion decay constant.Comment: Plain latex, 15 page

Nucleon form factors in the canonically quantized Skyrme model

The explicit expressions for the electric, magnetic, axial and induced pseudoscalar form factors of the nucleons are derived in the {\it ab initio} quantized Skyrme model. The canonical quantization procedure ensures the existence of stable soliton solutions with good quantum numbers. The form factors are derived for representations of arbitrary dimension of the SU(2) group. After fixing the two parameters of the model, $f_\pi$ and $e$, by the empirical mass and electric mean square radius of the proton, the calculated electric and magnetic form factors are fairly close to the empirical ones, whereas the the axial and induced pseudoscalar form factors fall off too slowly with momentum transfer.Comment: 14pp including figure

Closed form solution for a double quantum well using Gr\"obner basis

Analytical expressions for spectrum, eigenfunctions and dipole matrix elements of a square double quantum well (DQW) are presented for a general case when the potential in different regions of the DQW has different heights and effective masses are different. This was achieved by Gr\"obner basis algorithm which allows to disentangle the resulting coupled polynomials without explicitly solving the transcendental eigenvalue equation.Comment: 4 figures, Mathematica full calculation noteboo