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UNIVERSIDADE FEDERAL DO MARANHÃO
CENTRO DE CIÊNCIAS EXATAS E TECNOLOGIA
PROGRAMA DE PÓS-GRADUÇÃO EM FÍSICA
MÁRCIO DA SILVA TAVARES
ESTUDO DO POTENCIAL DE INTERAÇÃO ELÉTRON-ELÉTRON
NO CONTEXTO DA TEORIA DE MAXWELL-CHERN-SIMONS-
PROCA COM VIOLAÇÃO DE LORENTZ
São Luís
2006
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MÁRCIO DA SILVA TAVARES
ESTUDO DO POTENCIAL DE INTERAÇÃO ELÉTRON-ELÉTRON
NO CONTEXTO DA TEORIA DE MAXWELL-CHERN-SIMONS-
PROCA COM VIOLAÇÃO DE LORENTZ
Dissertação apresentada ao programa de Pós-
Graduação em Física da Universidade Federal do
Maranhão para obtenção do grau de mestre em
Física.
Orientador: Prof. Dr. Manoel Messias Ferreira
Junior
São Luís
2006
ads:
Tavares, Márcio da Silva.
Estudo do potencial de interação elétron-elétron no contexto da teoria de Maxwell-
Chern-Simons-Proca com violação de Lorentz / Márcio da Silva Tavares. – 2007.
91.
Texto impresso (fotocópia)
Orientador: Manoel Messias Ferreira Junior
Dissertação (Mestrado) – Programa de Pós-Graduação em Física, Universidade
Federal do Maranhão, 2007.
1. Eletróns. 2. Eletrodinâmica Planar. 3. I. Orientador: Ferreira Junior, Manoel
Messias. II. Título.
CDU 539.124
ESTUDO DO POTENCIAL DE INTERAÇÃO ELÉTRON-ELÉTRON
NO CONTEXTO DA TEORIA DE MAXWELL-CHERN-SIMONS-
PROCA COM VIOLAÇÃO DE LORENTZ
Dissertação apresentada ao programa de Pós-
Graduação em Física da Universidade Federal do
Maranhão para obtenção do grau de mestre em
Física.
Aprovada em 03/10/2006
BANCA EXAMINADORA
......................................................................................................................................
Prof. Dr. Manoel Messias Ferreira Jr
Doutor em Física
Universidade Federal do Maranhão – UFMA
........................................................................................................................................
Prof. Dr. Ricardo Renan Landim Carvalho
Doutor em Física
Universidade Federal do Ceará – UFC
..............................................................................................................................
Prof. Dr. Adalto Rodrigues Gomes
Doutor em Física
Centro Federal de Educação Tecnológica do Maranhão – CEFET-MA
DEDICATÓRIA
Dedico...
A DEUS,
a minha família,
a minha namorada,
aos companheiros.
AGRADECIMENTOS
Agradeço....
A Deus, por me conceder saúde e me iluminar durante toda a minha vida,
A meus pais, pela suas pelejas e constantes incentivos,
A minha irmã pela suas colaborações,
A minha namorada pela sua presença,
A meus colegas de labuta,
Ao professor Manoel Messias Ferreira Junior, pela sua colaboração e
paciência,
A Universidade Federal do Maranhão,
A Fapema, pelos seus incentivos.
“Tu és digno, Senhor e Deus nosso, de receber a glória,
a honra e o poder, porque criaste todas as coisas, e por
tua vontade elas existiram e foram criadas.”
Apocalipse 4:11.
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23 "5FA9F@=B;< &BB9G #9=89B CAA 6 67 
23 . $9=GGB9F 5B8 ) &7<G9B:9@8 %5HIFK=GG9BG7<5:H9B   
23 # % CCD9F '<MG )9J    ! 5F899B # % CDD9F 5B8 ! )
*7<F=9T9F '<MG )9J  
23 6F=?CGCJ *CJ '<MG!+'   
23 ! 98BCFN 5B8  $d@@9F 1 '<MG   
23 .% 58M 9H 5@ '<MG )9J #9HH    1/*<9B 9H 5@ =6=8  
  +GI9= 9H 5@ =6=8     *IB 9H 5@ '<MG )9J #9MM
  ""CINB9HGCJ 9H 5@ =6=8   
23  #=B89 )9D 'FC; '<MG     FCGG ) '=G5F?= 5B8 # 05T9 )9J
$C8 '<MG   
23 . *=9;9@ %I7@ '<MG    ) !57?=K * +9AD@9HCB '<MG )9J
   ! *7<CB:9@8 %I7@ '<MG    * 9G9F ) !57?=K
5B8 * +9AD@9HCB BB '<MG   
23 " J"@=HN=B; &  '<MG )9J #9HH    ) #5I;<@=B '<MG )9J 
   +GI= &  '<MG )9J #9HH    )  #5I;<@=B '<MG
)9J #9HH    C=G 9L79@9BH9G 5FH=;CG 89 F9J=GYC  C?= Q(I5BH=G98
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5@@ T97HR )9D 'FC; '<MG    * $ =FJ=B Q+<9 (I5BHIA 5@@
T97H %CJ9@ L7=H=CBG 5B8C FC?9B *=AA9HF=9GR 7CB8A5H
23 *  1<5B; + 5BGCB 5B8 * "=J9@GCB '<MG )9J #9HH    *  1<5B;
BH ! $C8 '<MG   
23 * $ 5FFC@   =9@8 5B8 ) !57?=K '<MG )9J   
23  C@@585M 5B8 -  "CGH9@97?e '<MG )9J    =6=8 '<MG )9J
 
23 -  "CGH9@97?M 5B8 * *5AI9@ '<MG )9J    -  "CGH9@97?M 5B8
) 'CHH=B; %I7@ '<MG    =6=8 '<MG #9HH    =6=8
'<MG )9J   
23 9@=7< + CGH5*C5F9G $$9FF9=F5 !F 5B8 !9@5M]@%9HC IF '<MG !
  
23 9@=7< &$ 9@ =A5 $$9FF9=F5 !F 5B8 !9@5M]@%9HC BH ! $C8 '<MG
  
23 '5\H5 *75FD9@@=  9@=7< !#C@8C #9@5M]@%9HC '<MG )9J  
  "CGH9@97?M )#9<B9FH 5B8 $ '9FFM =6=8   9@=7< 9H
5@ =6=8 
23  9@=7< $$9FF9=F5 !F!9@5M]@%9HC 5B8 $+ &F@5B8C '<MG )9J
   =6=8   
23 9@=7< $$9FF9=F5 !F!9@5M]@%9HC 5B8 $+ &F@5B8C '<MG )9J
  
23 $$9FF9=F5 !F '<MG )9J  
23 $$9FF9=F5 !F '<MG )9J  
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23 9@=7< $$9FF9=F5 !F !9@5M]@%9HC IF '<MG !  
23 0  "C;5B !+' #9HH  
23  FCG<9J 5B8 ) 'CDD=HN '<MG #9HH   
23 & =FCHH= &  '<MG )9J #9HH    & =FCHH= &  '<MG #9HH
  
23  ) 5;9B '<MG )9J      ) 5;9B '<MG )9J #9HH 

23 & =FCHH= &  '<MG )9J #9HH   
23 $  C6FC@=I6CJ  @=9N9F   "C;5B . *9A9BCT ) *N56C $C8 '<MG #9HH
  
23 5J=8 F=SH<G !&$"'&"! &"  !&$+ #$&% !C<B .=@9M *CBG B7 
 5@N9B   $5FH=B '$% #&"!% ! !&$"'&"$+ "'$% ! "$!
+%% !C<B .=@9M *CBG B7 
23 0 9CF;9@=B ! .5@@9H '<MG )9J   
23 ) 5;9B '<MG #9HH    &=FCHH= 9H 5@ '<MG )9J #9H  
 $ C6FC@=I6CJ 9M 5@ $C8 '<MG #9HH    FCG<9J 5B8 )
'CDD=HN '<MG #9HH     0 9CF;9@=B 5B8 ! .5@@9H '<MG )9J
  
23 9@=7< &$ 9@ =A5 $$9FF9=F5 !F 5B8 !9@5M]@%9HC IF '<MG ! 
   =6=8 ! '<MG  %I7@95F 5B8 '5FH=7@9 '<MG=7G   
23  <F=GH=5BG9B &$9@ =A5 $$9FF9=F5 !F 5B8 !9@5M]@%9HC BH ! $C8
'<MG   
23 ! ! *5?IF5= (! '!&' !% 88=GCB.9G@9M 'I6@=G<=B; CAD5BM

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23 ) !57?=K 5B8 -  "CGH9@97?e +% ( &&    !$ <IB; '<MG
#9HH     ! $ <IB; 5B8  " <IB; +% (  
 !$ <IB; '<MG )9J   $ '9F9N-=7HCF=5 +% (
&&    ) !57?=K 5B8 - "CGH9@97?M +% ( && 
 CBB95I '+%    $ '9F9N-=7HCF=5  
   ' 5\H5 *75FD9@@= &  +% (     @HG7<I@
'<MG )9J   )   F=HC + $5F=N !) %5G7=A9BHC
'5GGCG ) )=69=FC !'   
23  85A 5B8  ) "@=B?<5A9F ' +%     85A 5B8 )
"@=B?<5A9F '<MG #9HH   
23 - "CGH9@97?M 5B8 ) #9<B9FH '<MG )9J    ) #9<B9FH +%
(   
23 ) $CBH9A5MCF 5B8 # ,FFIH=5 +% (    (  5=@9M 5B8
-  "CGH9@97?M +% (   
23  B8F=5BCJ ) *C@85H= # *CF6C +% (    B8F=
5BCJ ' =577CB= 5B8 ) *C@85H= !'   
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