Relativistic lagrangian no-linear field theories supporting non-topological soliton solutions

Abstract

In this thesis we perform a broad study of a class of relativistic field theories supporting non-topological soliton solution in three space dimensions. More precisely, we study (multi-) scalar fields arising in theories whose lagrangians are defined as general functions of the standard kinetic term, and (abelian and non-abelian) gauge fields in generalize gauge field theories with lagrangian densities defined as functions of the two standard quadratic invariants of the field. In the scalar case we have obtained a complete characterization of the static, spherically symmetric solutions which are finite-energy (definite positive) and stable. In the gauge field case we have performed a general study which also leads to a characterization of the electrostatic spherically symmetric solutions which forms and energies can be shown to be related to their (multi-) scalar counterparts. Along the study, the condition of admissibility, which corresponds to several restrictions to be imposed on the lagrangian densities in order to obtain physically consistent field theories, plays a crucial role in the exhaustive determination of this class of soliton-supporting non-linear field theories. From the variational analysis of the energy functional and the study of the dynamic evolution of the perturbations are these solutions in the field equations, we have obtained necessary and sufficient conditions for these (multi-) scalar and gauge solutions to be weakly stable, i.e. stable against small charge-preserving perturbations. Moreover, several explicit examples of lagrangians belonging to this class of theories have been introduced. These lagrangians have been analyzed in great detail, and we have obtained a complete description of their energies and other physically relevant properties. A particular example of this class of non-linear lagrangian field models is the Born-Infeld theory. Finally we have studied several applications that this class of lagrangians with non-topological solitons can have in diverse contexts, such as self-gravitating (scalar, abelian, non-abelian) soliton solutions or the phenomenological descripcion of the hadron internal structure and the hadronic interactions. Many other applications can be also envisaged from several results obtained in this work including soliton solutions within effective models of Quantum Electrodynamics, short-range behaviours, electric-magnetic dualities, etc.