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Title: A study on relativistic lagrangian field theories with non-topological soliton solutions

Abstract

We perform a general analysis of the dynamic structure of two classes of relativistic lagrangian field theories exhibiting static spherically symmetric non-topological soliton solutions. The analysis is concerned with (multi-) scalar fields and generalized gauge fields of compact semi-simple Lie groups. The lagrangian densities governing the dynamics of the (multi-) scalar fields are assumed to be general functions of the kinetic terms, whereas the gauge-invariant lagrangians are general functions of the field invariants. These functions are constrained by requirements of regularity, positivity of the energy and vanishing of the vacuum energy, defining what we call 'admissible' models. In the scalar case we establish the general conditions which determine exhaustively the families of admissible lagrangian models supporting this kind of finite-energy solutions. We analyze some explicit examples of these different families, which are defined by the asymptotic and central behaviour of the fields of the corresponding particle-like solutions. From the variational analysis of the energy functional, we show that the admissibility constraints and the finiteness of the energy of the scalar solitons are necessary and sufficient conditions for their linear static stability against small charge-preserving perturbations. Furthermore, we perform a general spectral analysis of the dynamic evolution of the small perturbationsmore » around the statically stable solitons, establishing their dynamic stability. Next, we consider the case of many-components scalar fields, showing that the resolution of the particle-like field problem in this case reduces to that of the one-component case. The study of these scalar models is a necessary step in the analysis of the gauge fields. In this latter case, we add the requirement of parity invariance to the admissibility constraints. We determine the general conditions defining the families of admissible gauge-invariant models exhibiting finite-energy electrostatic spherically symmetric solutions which, unlike the (multi-) scalar case, are not always stable. The variational analysis of the energy functional leads now to supplementary restrictions to be imposed on the lagrangian densities in order to ensure the linear stability of the solitons. We establish a correspondence between any admissible soliton-supporting (multi-) scalar model and a family of admissible generalized gauge models supporting finite-energy electrostatic point-like solutions. Conversely, for each admissible soliton-supporting gauge-invariant model there is an associated unique admissible (multi-) scalar model with soliton solutions. This shows the exhaustive character of the admissibility and stability conditions in determining the class of soliton-supporting generalized gauge models. The usual Born-Infeld electrodynamic theory and its non-abelian extensions are shown to be (very particular) examples of one of these families.« less

Authors:
 [1];  [2]
  1. LUTH, Observatoire de Paris, CNRS, Universite Paris Diderot, 5 Place Jules Janssen, 92190 Meudon (France)
  2. Departamento de Fisica, Universidad de Oviedo, Avda. Calvo Sotelo 18, E-33007 Oviedo, Asturias (Spain)
Publication Date:
OSTI Identifier:
21167730
Resource Type:
Journal Article
Journal Name:
Annals of Physics (New York)
Additional Journal Information:
Journal Volume: 324; Journal Issue: 4; Other Information: DOI: 10.1016/j.aop.2008.09.008; PII: S0003-4916(08)00150-4; Copyright (c) 2008 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0003-4916
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ASYMPTOTIC SOLUTIONS; BORN-INFELD THEORY; EVOLUTION; GAUGE INVARIANCE; LAGRANGIAN FIELD THEORY; LAGRANGIAN FUNCTION; LIE GROUPS; NONLINEAR PROBLEMS; PARITY; PERTURBATION THEORY; RELATIVISTIC RANGE; SCALAR FIELDS; SCALARS; SOLITONS; TOPOLOGY; VARIATIONAL METHODS

Citation Formats

Diaz-Alonso, J, Departamento de Fisica, Universidad de Oviedo, Avda. Calvo Sotelo 18, E-33007 Oviedo, Asturias, and Rubiera-Garcia, D. A study on relativistic lagrangian field theories with non-topological soliton solutions. United States: N. p., 2009. Web. doi:10.1016/j.aop.2008.09.008.
Diaz-Alonso, J, Departamento de Fisica, Universidad de Oviedo, Avda. Calvo Sotelo 18, E-33007 Oviedo, Asturias, & Rubiera-Garcia, D. A study on relativistic lagrangian field theories with non-topological soliton solutions. United States. https://doi.org/10.1016/j.aop.2008.09.008
Diaz-Alonso, J, Departamento de Fisica, Universidad de Oviedo, Avda. Calvo Sotelo 18, E-33007 Oviedo, Asturias, and Rubiera-Garcia, D. 2009. "A study on relativistic lagrangian field theories with non-topological soliton solutions". United States. https://doi.org/10.1016/j.aop.2008.09.008.
@article{osti_21167730,
title = {A study on relativistic lagrangian field theories with non-topological soliton solutions},
author = {Diaz-Alonso, J and Departamento de Fisica, Universidad de Oviedo, Avda. Calvo Sotelo 18, E-33007 Oviedo, Asturias and Rubiera-Garcia, D},
abstractNote = {We perform a general analysis of the dynamic structure of two classes of relativistic lagrangian field theories exhibiting static spherically symmetric non-topological soliton solutions. The analysis is concerned with (multi-) scalar fields and generalized gauge fields of compact semi-simple Lie groups. The lagrangian densities governing the dynamics of the (multi-) scalar fields are assumed to be general functions of the kinetic terms, whereas the gauge-invariant lagrangians are general functions of the field invariants. These functions are constrained by requirements of regularity, positivity of the energy and vanishing of the vacuum energy, defining what we call 'admissible' models. In the scalar case we establish the general conditions which determine exhaustively the families of admissible lagrangian models supporting this kind of finite-energy solutions. We analyze some explicit examples of these different families, which are defined by the asymptotic and central behaviour of the fields of the corresponding particle-like solutions. From the variational analysis of the energy functional, we show that the admissibility constraints and the finiteness of the energy of the scalar solitons are necessary and sufficient conditions for their linear static stability against small charge-preserving perturbations. Furthermore, we perform a general spectral analysis of the dynamic evolution of the small perturbations around the statically stable solitons, establishing their dynamic stability. Next, we consider the case of many-components scalar fields, showing that the resolution of the particle-like field problem in this case reduces to that of the one-component case. The study of these scalar models is a necessary step in the analysis of the gauge fields. In this latter case, we add the requirement of parity invariance to the admissibility constraints. We determine the general conditions defining the families of admissible gauge-invariant models exhibiting finite-energy electrostatic spherically symmetric solutions which, unlike the (multi-) scalar case, are not always stable. The variational analysis of the energy functional leads now to supplementary restrictions to be imposed on the lagrangian densities in order to ensure the linear stability of the solitons. We establish a correspondence between any admissible soliton-supporting (multi-) scalar model and a family of admissible generalized gauge models supporting finite-energy electrostatic point-like solutions. Conversely, for each admissible soliton-supporting gauge-invariant model there is an associated unique admissible (multi-) scalar model with soliton solutions. This shows the exhaustive character of the admissibility and stability conditions in determining the class of soliton-supporting generalized gauge models. The usual Born-Infeld electrodynamic theory and its non-abelian extensions are shown to be (very particular) examples of one of these families.},
doi = {10.1016/j.aop.2008.09.008},
url = {https://www.osti.gov/biblio/21167730}, journal = {Annals of Physics (New York)},
issn = {0003-4916},
number = 4,
volume = 324,
place = {United States},
year = {Wed Apr 15 00:00:00 EDT 2009},
month = {Wed Apr 15 00:00:00 EDT 2009}
}