RT info:eu-repo/semantics/doctoralThesis
T1 Dynamics and Interaction of Solitons in the BPS Limit and their Internal Modes
A1 Navarro Obregón, Sergio
A2 Universidad de Valladolid. Escuela de Doctorado
K1 Solitons
K1 Topological Solitons
K1 Solitones Topológicos
K1 Nonlinear Physics
K1 Física No Lineal
K1 Classical Field Theory
K1 Teoría Clásica de Campos
K1 Pertubative Theory
K1 Teoría de Perturbaciones
K1 22 Física
AB Solitons are special solutions of nonlinear classical field theories that behave like extended particle-like states. They are of considerable interest both in classical physics and quantum field theory, with applications ranging from condensed matter and nuclear physics to cosmology. These non-perturbative objects can be classified as stable or unstable, depending on whether they display dispersive behaviour. Stable solitons fall into two broad categories. Topological solitons, such as kinks, vortices, and monopoles, derive their stability from topological invariants. Within the class of field theories that admit topological solitons, BPS theories (Bogomolny–Prasad–Sommerfield) are especially notable, since their solitons exhibit no static interactions, allowing multiple configurations to exist with the same energy. BPS solutions satisfy first-order differential equations that automatically solve the static Euler-Lagrange equations. In contrast, non-topological solitons —including Q-balls, soliton stars, and oscillons— are stabilised by conserved charges of global symmetries, by the integrability of the theory, or by specific adiabatic invariants. Finally, unstable solitons, such as sphalerons, represent metastable configurations. Solitons also possess a rich internal structure, which can be understood in terms of collective excitations around the base configuration. These excitations may lead to fragmentation into more elementary entities, oscillations that modify the soliton’s size, or new dynamical behaviours during its evolution. Such modes may be triggered after a phase transition or during interactions with other solitons, impurities, or incoming radiation. The main purpose of this thesis has been to examine soliton dynamics, with particular attention to the role of internal modes. The research has focused on one- and two-dimensional models, providing a foundation for extending the analysis to three-dimensional theories. Among the wide variety of solitons, this thesis concentrates on kinks, oscillons, vortices, and sphalerons. Nevertheless, field theories possess infinitely many degrees of freedom, which makes both analytic solutions and predictive modelling highly challenging. To address this, the work develops effective models that retain only the essential degrees of freedom, employing the well-established collective coordinate method. Additional tools, such as perturbative techniques, have also been applied. Among the main contributions, it is worth highlighting, first, the incorporation—for the first time within the collective coordinate framework—of genuine radiation modes, which makes it possible to describe phenomena of radiation emission and interaction in solitonic systems. Secondly, a generalisation of Samols’ moduli space metric for local vortices in the Abelian–Higgs model has been achieved by incorporating vibrational degrees of freedom. This extension allows the construction of accurate initial conditions for effective models of vortex–vortex collisions. Moreover, a new class of sphalerons, termed semi-BPS sphalerons, has been identified and studied. These exhibit properties closely analogous to those of BPS solitons. Finally, the role of oscillatory internal modes in the decay process of sphalerons has been studied in detail, leading to the proposal of a dynamic stabilisation mechanism. This mechanism has been further explained and extended to more general models, demonstrating the robustness and potential applicability of this phenomenon to physically relevant theories.
YR 2026
FD 2026
LK https://uvadoc.uva.es/handle/10324/83395
UL https://uvadoc.uva.es/handle/10324/83395
LA eng
NO Escuela de Doctorado
DS UVaDOC
RD 11-mar-2026