Inhomogeneous solutions in semiclassical field theory

The applicability of the semiclassical approach to the description of dilute systems and models with weak coupling will be discussed. First, we will consider Rosen's analytical model, which allows us to construct an exact solution for nontopological solitons. Secondly, this model will be interpreted within the framework of effective theory and a correspondence between the Rosen model and the Friedberg-Lee-Sirlin theory will be presented [1,2]. Then some issues of linear stability of nontopological solitons in the presence of a gauge field will be discussed [3].
In the talk we will also discuss non-topological solitons in non-relativistic theory in (1+1) and (2+1) dimensions [4,5]. Remarkably, in the case of some self-action potentials, the symmetry group of the theory is significantly larger than the usual Galilean group. Thus, invariance arises with respect to scale and special conformal transformations, which leads to additional degeneracy in the spectrum of soliton solutions. Then we will discuss the relativistic completion of such models and the effect of the gauge field on solitons in the (2+1)-dimensional theory [6,7].
[1] Kim, E., & Nugaev, E. (2024). Effectively flat potential in the Friedberg–Lee–Sirlin model. The European Physical Journal C, 84(8), 797.
[2] Kim, E., Nugaev, E., & Shnir, Y. (2024). Large solitons flattened by small quantum corrections. Physics Letters B, 856, 138881.
[3] Galushkina, Y., Kim, E., Nugaev, E., & Shnir, Y. (2025). Localized electromagnetic perturbations on vector solitons. Phys.Lett.B 865 (2025) 139469
[4] Galushkina, Y., Kim, E., Nugaev, E., & Shnir, Y. (2025). Properties of Non-topological Solitons in Two-dimensional Model With Resurrected Conformal Symmetry. Europhysics Letters, 151(6), 64002.
[5] Galushkina, Y., Kim, E., Nugaev, E., & Shnir, Y. (2025). CFT approach to rotating field lumps in an attractive potential. Physical Review D, 112(7), 076019.
[6] Galushkina, Y., Kim, E., Nugaev, E., & Shnir, Y. (2025). Stable Rotating Solitons in UV-completed Models. arXiv preprint arXiv:2511.xxxx.
[7] Ivashkin, I., Kim, E., Nugaev, E., & Shnir, Y. (2025). Towards Gauged Non-topological Solitons in the Model with Chern-Simons Term. arXiv preprint arXiv:2511.xxxx.