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Previous issue date: 2016-12-16 / We study self-dual con gurations solutions for gauge models in the context of the Standard
Model Extension and in abelian Higgs generalized models. First we approach the Maxwell-
Higgs model provided with Lorentz symmetry violation (VL) terms in two situations: In the
rst case, we add the Carroll-Field-Jackiw (CPT-odd) term into the gauge sector and another
CPT-even term in the Higgs sector. In the second case, we add CPT-even terms in both sectors.
For both cases the Lorentz symmetry breaking terms modi ed the kinetic part of the eld.
The con gurations in the presence of the Carroll-Field-Jackiw (CFJ) term have non-zero total
electric charge as well as proportional to the magnetic
ux, while the con gurations containing
only CPT-even terms have null electrical charge. However, the solutions obtained when we
consider the gauge sector with CPT-even and parity-odd coe cients have non-zero electric
eld. The implementation of the BPS formalism provides self-dual equations whose solutions
have total energy proportional to the magnetic
ux. We have studied in detail the axially
symmetrical v ortices-like solutions using the appropriate ansatz. We note that the magnetic
ux
as well as being proportional to the winding number, also depends on the CPT-even coe cients
of the Higgs sector. We show that there exist a sets of valuesfor the CPT-even coe cients of
Higgs sector that reproduce the con gurations for the abelian Higgs models already studied in
literature. Another important result is the existence of a set of parameters involving only the
CPT-even case, in which the BPS (Bogomoln'yi-Prasad-Sommer eld) v ortices exhibit localized
inversion of both magnetic and electric eld.
In the second chapter, still in the context of Lorentz invariance symmetry violation, we
study the self-dual con gurations in the O (3) nonlinear sigma model coupled to a gauge eld.
The usual model is modi ed by introducing the CPT-odd term of CFJ in the gauge sector and a
CPT-even term in the sigma sector, both modifying only the kinetic sectors. The con gurations
have non-null total charge and are proportional to the magnetic
ux. The BPS formalism
provides the self-dual equations with con gurations having total energy proportional to the
topological charge of the model. Then we study the axially symmetric v ortices solutions. These
have total energy proportional to the winding number and depends on the Lorentz violation
coe cients belonging to the sigma sector. This dependence is re
ected in the topological charge
and in the magnetic
ux. Similarly to the previous case, there exist a set of values for the CPTeven
coe cients of the sigma sector that interpolate the con gurations of usual O (3) nonlinear
sigma models coupled to a gauge eld already found in literature.
On the third and nal part of this manuscript we study the existence of self-dual con -
gurations in models for abelian Higgs generalized models: Maxwell-Higgs, Born-Infeld-Higgs,
Chern-Simons-Higgs and Maxwell-Chern-Simons-Higgs. The generalization modi es the kinetics
of the elds by means of functions that depend only on the Higgs eld ( ). During the
development of the implementation of the BPS formalism, naturally arises the explicit function
that generalize the kinetic term of the Higgs eld, j j2 2; > 1. Thus, we are able to
determined the self-dual potential and the corresponding rst order equations for each model.
Among the self-dual con gurations, we study the vortex-like solutions and found that from
a given value of the parameter the pro les begin to acquire a shape similar to the form of
compactons-like solutions. / Estudamos as con gurafigurações auto-duais em modelos de gauge no contexto do Modelo Padrão
Estendido e em modelos de Higgs abelianos generalizados. Primeiramente abordamos o modelo
de Maxwell-Higgs provido com termos de violalação da invariância de Lorentz (VL) em duas
situações: No primeiro caso, adicionamos o termo de Carroll-Field-Jackiw (CPT- mpar) ao setor
de gauge e um outro termo CPT-par no setor de Higgs. No segundo caso, inserimos termos CPTpar
em ambos os setores. Em todos os casos os termos da quebra de Lorentz modi cam a parte
cin etica dos campos. As con gura c~oes na presen ca do termo de Carroll-Field-Jackiw (CFJ) tem
carga el etrica total n~ao nula, al em de serem proporcionais ao
uxo magn etico, enquanto que
as con gura c~oes contendo somente termos CPT-par tem carga el etrica total nula. Contudo, as
solu c~oes obtidas quando consideramos o setor de gauge com coe cientes CPT-par de paridade-
mpar possuem campo el etrico n~ao nulo. A implementa c~ao do formalismo BPS prov^e equa c~oes
auto-duais cujas solu c~oes tem energia total proporcional ao
uxo magn etico. Estudamos em
detalhe as solu c~oes tipo v ortices axialmente sim etricos usando o ansatz apropriado. Observamos
que o
uxo magn etico al em de ser proporcional ao n umero de vorticidade, tamb em depende
dos coe cientes CPT-par do setor de Higgs. Mostramos que existem conjuntos de valores dos
coe cientes CPT-par do setor de Higgs que reproduzem as con gura c~oes dos modelos de Higgs
abelianos j a estudados na literatura. Um outro resultado importante e a exist^encia de um
jogo de par^ametros envolvendo o caso puramente CPT-par cujos v ortices BPS (Bogomoln'yi-
Prasad-Sommer eld) apresentam a invers~ao localizada tanto do campo magn etico como do
campo el etrico.
Ainda no contexto de VL, estudamos as con gura c~oes auto-duais num modelo n~ao abeliano:
o modelo O(3) sigma n~ao-linear acoplado a um campo de gauge. O modelo usual e modi cado
introduzindo o termo CPT- mpar de CFJ no setor de gauge e um termo CPT-par no setor
sigma, ambos modi cando somente os setores cin eticos. As con gura c~oes tem carga total
n~ao nula proporcional ao
uxo magn etico. O formalismo BPS fornece as equa c~oes auto-duais
com con gura c~oes possuindo energia total proporcional a carga topol ogica do modelo. Em
seguida, estudamos as solu c~oes de v ortices axialmente sim etricos. Estes possuem energia total
proporcional a vorticidade e depende dos coe cientes VL pertencentes ao setor sigma. Essa
depend^encia e re
etida na carga topol ogica e no
uxo magn etico. Similarmente ao caso anterior,
existem conjuntos de valores dos coe cientes CPT-par do setor de sigma permitem interpolar as
con gura c~oes dos modelos O(3) sigma n~ao-linear acoplado a um campo de gauge encontrados
na literatura.
Finalmente, no contexto de teorias de campo invariantes de Lorentz, estudamos a exist^encia
de con gura c~oes auto-duais nos modelos de Higgs abelianos generalizados: Maxwell-Higgs,
Born-Infeld-Higgs, Chern-Simons-Higgs e Maxwell-Chern-Simons-Higgs. A generaliza c~ao modi-
ca a parte cin etica dos campos por meio de fun c~oes que dependem somente do campo de Higgs
( ). Durante o desenvolvimento da implementa c~ao do formalismo BPS, naturalmente surge a
forma expl cita da fun c~ao que generaliza o termo cin etico do campo de Higgs, j j2 2; > 1.
Com isso, determinados os potenciais auto-duais e as correspondentes equa c~oes de primeira ordem
para cada modelo. Dentre as con gura c~oes auto-duais, estudamos as solu c~oes tipo v ortice
e encontramos que a partir de um determinado valor do par^ametro os per s come cam a
adquirir forma semelhante as das solu c~oes do tipo-compactons.
| Identifer | oai:union.ndltd.org:IBICT/oai:tede2:tede/1234 |
| Date | 16 December 2016 |
| Creators | Mentech, Guillermo Lazar |
| Contributors | CASANA SIFUENTES, Rodolfo Alván |
| Publisher | Universidade Federal do Maranhão, PROGRAMA DE PÓS-GRADUAÇÃO EM FÍSICA/CCET, UFMA, Brasil, Física |
| Source Sets | IBICT Brazilian ETDs |
| Language | Portuguese |
| Detected Language | English |
| Type | info:eu-repo/semantics/publishedVersion, info:eu-repo/semantics/doctoralThesis |
| Format | application/pdf |
| Source | reponame:Biblioteca Digital de Teses e Dissertações da UFMA, instname:Universidade Federal do Maranhão, instacron:UFMA |
| Rights | http://creativecommons.org/licenses/by-nc-nd/4.0/, info:eu-repo/semantics/openAccess |
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