❯♥✐✈❡rs✐❞❛❞❡ ❞❡ ❙ã♦ P❛✉❧♦ ■♥st✐t✉t♦ ❞❡ ❋ís✐❝❛
❆♥á❧♦❣♦s ❈♦s♠♦❧ó❣✐❝♦s ❞♦s ❊❢❡✐t♦s ❙❝❤✇✐♥❣❡r
❊stát✐❝♦ ❡ ❖s❝✐❧❛tór✐♦
❊❧✐s❛ ●♦✉✈ê❛ ▼❛✉r✐❝✐♦ ❋❡rr❡✐r❛
❖r✐❡♥t❛❞♦r✿ Pr♦❢✳ ❉r✳ ▲✉✐s ❘❛✉❧ ❲❡❜❡r ❆❜r❛♠♦ ❉✐ss❡rt❛çã♦ ❞❡ ▼❡str❛❞♦ ❛♣r❡s❡♥t❛❞❛ ❛♦
■♥st✐t✉t♦ ❞❡ ❋ís✐❝❛ ❞❛ ❯♥✐✈❡rs✐❞❛❞❡ ❞❡ ❙ã♦ P❛✉❧♦ ♣❛r❛ ❛ ♦❜t❡♥çã♦ ❞♦ tít✉❧♦ ❞❡ ▼❡str❡ ❡♠ ❈✐ê♥❝✐❛s✳
❇❛♥❝❛ ❊①❛♠✐♥❛❞♦r❛✿
Pr♦❢✳ ❉r✳ ▲✉✐s ❘❛✉❧ ❲❡❜❡r ❆❜r❛♠♦ ✭■❋❯❙P✮ Pr♦❢✳ ❉r✳ ❘♦❣ér✐♦ ❘♦s❡♥❢❡❧❞ ✭❯◆❊❙P✮ Pr♦❢❛✳ ❉r❛✳ ▼❛r✐❛ ❈❛r♦❧✐♥❛ ◆❡♠❡s ✭❯❋▼●✮
FICHA CATALOGRÁFICA
Preparada pelo Serviço de Biblioteca e Informação
do Instituto de Física da Universidade de São Paulo
Ferreira, Elisa Gouvêa Mauricio
Análogos cosmológicos dos efeitos Schwinger estático e oscilatório. São Paulo, 2009.
Dissertação (Mestrado) – Universidade de São Paulo. Instituto de Física, Departamento de Física Matemática.
Orientador: Prof. Dr. Luís Raul Weber Abramo
Área de Concentração: Física
Unitermos: 1. Cosmologia; 2.Universo primordial; 3. Teoria quântica de campo.
❘❡s✉♠♦
◆❡st❡ tr❛❜❛❧❤♦ ❡st✉❞❛♠♦s ♦s ❡❢❡✐t♦s q✉â♥t✐❝♦s ❞❡ ❝r✐❛çã♦ ❞❡ ♣❛rtí❝✉❧❛s ♥♦s ❝♦♥t❡①t♦s ❝♦s♠♦❧ó❣✐❝♦ ❡ ❞❛ ❡❧❡tr♦❞✐♥â♠✐❝❛ ❝❧áss✐❝❛✳ ❈♦♠ ♦ ❡st✉❞♦ ❞❛ ❝r✐❛çã♦ ❞❡ ♣❛rtí❝✉❧❛s ❡♠ ❝❛♠♣♦ ❡❧étr✐❝♦s ❡①t❡r♥♦s ❝♦♥st❛♥t❡s ❡ ♦s❝✐❧❛tór✐♦s✱ ♦s ❝♦♥❤❡❝✐❞♦s ❡❢❡✐t♦s ❙❝❤✇✐♥❣❡r ❡stát✐❝♦ ❡ ♦s❝✐❧❛tór✐♦✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✱ ❢♦✐ ♣♦ssí✈❡❧ ❡st✉❞❛r ❛ ♣♦❧❛r✐③❛çã♦ ❞♦ ✈á❝✉♦ q✉â♥t✐❝♦ ❡ ❛ ❝♦♥s❡qü❡♥t❡ ❝r✐❛çã♦ ❞❡ ♣❛rtí❝✉❧❛s ❞♦ ✈á❝✉♦✳ ❊ss❡ é ✉♠ ❡❢❡✐t♦ ♥ã♦✲♣❡rt✉r❜❛t✐✈♦ ♥♦ ❝♦♥t❡①t♦ ❞❛ ❡❧❡tr♦❞✐♥â♠✐❝❛ ❡ s✉❛ ♦❜s❡r✈❛çã♦ s❡r✐❛ ❞❡ ❣r❛♥❞❡ ✐♠♣♦rtâ♥❝✐❛ ♣❛r❛ ✈❛❧✐❞❛r ❡ss❛ t❡♦r✐❛ ♥❡ss❡ r❡❣✐♠❡✳
❊ss❡ ❡❢❡✐t♦✱ ♥♦ ❡♥t❛♥t♦✱ ❛✐♥❞❛ ♥ã♦ ❢♦✐ ❞❡t❡❝t❛❞♦ ❡①♣❡r✐♠❡♥t❛❧♠❡♥t❡✱ ✉♠❛ ✈❡③ q✉❡ sã♦ ♥❡❝❡ssár✐♦s ❝❛♠♣♦s ❡❧étr✐❝♦s ♠✉✐t♦ ❢♦rt❡s ♥♦ ❝❛s♦ ❡stát✐❝♦✳ ❈♦♥t✉❞♦✱ ♥♦ ❝❛s♦ ♦s❝✐❧❛tór✐♦ ❡①✐st❡ ✉♠ ❡①♣❡r✐♠❡♥t♦ ❡♠ ❛♥❞❛♠❡♥t♦ ♣❛r❛ ❛ ❞❡t❡❝çã♦ ❞❡ ✉♠ ❡❢❡✐t♦ q✉â♥t✐❝♦ ❛♥á❧♦❣♦✱ ♦ ❝❤❛♠❛❞♦ ❡❢❡✐t♦ ❈❛s✐♠✐r ❞✐♥â♠✐❝♦✳ ❆ ✈❡r✐✜❝❛çã♦ ❞♦ ❡❢❡✐t♦ ❈❛s✐♠✐r ❞✐♥â♠✐❝♦ é ✐♠♣♦rt❛♥t❡ ♣❛r❛ ❛ ✈❛❧✐❞❛çã♦ ❞♦ ❡❢❡✐t♦ ❙❝❤✇✐♥❣❡r ♦s❝✐❧❛tór✐♦✱ ❞❛❞♦ q✉❡ ♦ ♠♦✈✐♠❡♥t♦ ❞❛s ❝♦♥❞✐çõ❡s ❞❡ ❝♦♥t♦r♥♦ é ❡q✉✐✈❛❧❡♥t❡ à ❛♣❧✐❝❛çã♦ ❞❡ ✉♠ ❝❛♠♣♦ ❡①t❡r♥♦✳
❋✐♥❛❧♠❡♥t❡✱ ❢♦✐ ❡st✉❞❛❞❛ ❛ ❝r✐❛çã♦ ❞❡ ♣❛rtí❝✉❧❛s ❡♠ ✉♠ ❝♦♥t❡①t♦ ❝♦s♠♦❧ó❣✐❝♦✱ s❡♥❞♦ ♦ ❝❛s♦ ❡stát✐❝♦ ❛ ❝r✐❛çã♦ ❞❡ ♣❛rtí❝✉❧❛s ♥❛ ❡r❛ ✐♥✢❛❝✐♦♥ár✐❛ ❞♦ ✉♥✐✈❡rs♦✳ ❖ ❝❛s♦ ❞✐♥â♠✐❝♦ ❝♦rr❡s♣♦♥❞❡ ❛♦ ♣❡rí♦❞♦ ❞❡ r❡❛q✉❡❝✐♠❡♥t♦ ♦✉✱ ♠❛✐s ♣r❡❝✐s❛♠❡♥t❡✱ ❡♠ s❡✉ ♣❡rí♦❞♦ ✐♥✐❝✐❛❧ ❝♦♥❤❡❝✐❞♦ ❝♦♠♦ ♣ré✲❛q✉❡❝✐♠❡♥t♦✱ ❡♠ q✉❡ ❛ ❝r✐❛çã♦ ❞❡ ♣❛rtí❝✉❧❛s é ♠❛✐s ❡✜❝✐❡♥t❡✳ ❆ ❝r✐❛çã♦ ❞❡ ♣❛rtí❝✉❧❛s ♥❛ ❡r❛ ✐♥✢❛❝✐♦♥ár✐❛ ♦❝♦rr❡ ❞❡✈✐❞♦ à ❡①♣❛♥sã♦ ❛❝❡❧❡r❛❞❛ ❞♦ ✉♥✐✈❡rs♦✳ P♦r ♠❡✐♦ ❞❡ ✉♠❛ tr❛♥s❢♦r♠❛çã♦ ❝❛♥ô♥✐❝❛ s✐♠♣❧❡s ❢♦✐ ♣♦ssí✈❡❧ ♦❜s❡r✈❛r q✉❡ ♦ ♠❡❝❛♥✐s♠♦ ❞❡ ❝r✐❛çã♦ ❞❡ ♣❛rtí❝✉❧❛s ♥❡ss❡ ♣❡rí♦❞♦ é ♦ ♠❡s♠♦ ❞❛ ❝r✐❛çã♦ ❞❡ ♣❛rtí❝✉❧❛s ❞♦ ❡❢❡✐t♦ ❙❝❤✇✐♥❣❡r ❡stát✐❝♦✳ ❉❛ ♠❡s♠❛ ❢♦r♠❛✱ ♣❛r❛ ♦ ♣ré✲❛q✉❡❝✐♠❡♥t♦✱ ❡♠ q✉❡ ❛ ❝r✐❛çã♦ ❞❡ ♣❛rtí❝✉❧❛s é ❞❛❞❛ ♣❡❧❛ ♦s❝✐❧❛çã♦ ❞♦ ✐♥✢❛t♦♥ ❡♠ t♦r♥♦ ❞❡ s❡✉ ♠í♥✐♠♦ ❞♦ ♣♦t❡♥❝✐❛❧✱ ♦ ♠❡❝❛♥✐s♠♦ ❞❡ ❝r✐❛çã♦ r❡s✉♠❡✲s❡ ❛ ✉♠ ♠❡❝❛♥✐s♠♦ ❞❡ r❡ss♦♥â♥❝✐❛ ♣❛r❛♠étr✐❝❛ ❞❡s❝r✐t♦ ♣♦r ✉♠❛ ❡q✉❛çã♦ ❞❡ ▼❛t❤✐❡✉✳ ❊ss❡ é ❡①❛t❛♠❡♥t❡ ♦ ♠❡s♠♦ ♠❡❝❛♥✐s♠♦ q✉❡ ❞❡s❝r❡✈❡ ❛ ❝r✐❛çã♦ ❞❡ ♣❛rtí❝✉❧❛s ♥♦ ❝❛s♦ ❞♦ ❡❢❡✐t♦ ❙❝❤✇✐♥❣❡r ♦s❝✐❧❛tór✐♦✳
❆❜str❛❝t
■♥ t❤✐s ✇♦r❦ ✇❡ st✉❞② t❤❡ q✉❛♥t✉♠ ❡✛❡❝ts ♦❢ ♣❛rt✐❝❧❡ ❝r❡❛t✐♦♥ ✐♥ t❤❡ ❝♦s♠♦❧♦❣✐❝❛❧ ❝♦♥t❡①t ❛♥❞ ♦❢ t❤❡ ❝❧❛ss✐❝❛❧ ❡❧❡❝tr♦❞②♥❛♠✐❝s✳ ❲✐t❤ t❤❡ st✉❞✐❡s ♦❢ t❤❡ ♣❛rt✐❝❧❡ ❝r❡❛t✐♦♥ ✐♥ ❝♦♥st❛♥t ❛♥❞ ♦s❝✐❧❧❛t♦r② ❡①t❡r♥❛❧ ❡❧❡❝tr✐❝❛❧ ✜❡❧❞s✱ t❤❡ ❦♥♦✇♥ st❛t✐❝ ❛♥❞ ♦s❝✐❧❧❛t♦r② ❙❝❤✇✐♥✲ ❣❡r ❡✛❡❝ts✱ r❡s♣❡❝t✐✈❡❧②✱ ✐t ✇❛s ♣♦ss✐❜❧❡ t♦ st✉❞② t❤❡ ♣♦❧❛r✐③❛t✐♦♥ ♦❢ t❤❡ q✉❛♥t✉♠ ✈❛❝✉✉♠ ❛♥❞ t❤❡ ❝♦♥s❡q✉❡♥t❧② ❝r❡❛t✐♦♥ ♦❢ ♣❛rt✐❝❧❡s ❢r♦♠ t❤❡ ✈❛❝✉✉♠✳ ❚❤✐s ✐s ❛ ♥♦♥ ♣❡rt✉r❜❛✲ t✐✈❡ ❡✛❡❝t ✐♥ t❤❡ ❝♦♥t❡①t ♦❢ t❤❡ ❡❧❡❝tr♦❞②♥❛♠✐❝s ❛♥❞ ✐ts ♦❜s❡r✈❛t✐♦♥ ✇♦✉❧❞ ❜❡ ♦❢ ❣r❡❛t ✐♠♣♦rt❛♥❝❡ t♦ ✈❛❧✐❞❛t❡ t❤✐s t❤❡♦r② ✐♥ t❤✐s r❡❣✐♠❡✳
❚❤✐s ❡✛❡❝t✱ ❤♦✇❡✈❡r✱ ✇❛s ♥♦t ②❡t ❡①♣❡r✐♠❡♥t❛❧❧② ❞❡t❡❝t❡❞✱ s✐♥❝❡ ✈❡r② str♦♥❣ ❡❧❡❝tr✐❝ ✜❡❧❞s ❛r❡ ♥❡❝❡ss❛r② ✐♥ t❤❡ st❛t✐❝ ❝❛s❡✳ ❍♦✇❡✈❡r✱ ✐♥ t❤❡ ♦s❝✐❧❧❛t♦r② ❝❛s❡ t❤❡r❡ ✐s ❛♥ ❡①✲ ♣❡r✐♠❡♥t ❝✉rr❡♥t❧② ✐♥ ❞❡✈❡❧♦♣♠❡♥t ❢♦r t❤❡ ❞❡t❡❝t✐♦♥ ♦❢ ❛♥ ❛♥❛❧♦❣ q✉❛♥t✉♠ ❡✛❡❝t ❝❛❧❧❡❞ ❞②♥❛♠✐❝❛❧ ❈❛s✐♠✐r ❡✛❡❝t✳ ❚❤❡ ✈❡r✐✜❝❛t✐♦♥ ♦❢ t❤❡ ❞②♥❛♠✐❝❛❧ ❈❛s✐♠✐r ❡✛❡❝t ✐s ✐♠♣♦rt❛♥t ❢♦r t❤❡ ✈❛❧✐❞❛t✐♦♥ ♦❢ t❤❡ ♦s❝✐❧❧❛t♦r② ❙❝❤✇✐♥❣❡r ❡✛❡❝t✱ s✐♥❝❡ t❤❡ ♠♦✈❡♠❡♥t ♦❢ t❤❡ ❜♦✉♥❞❛r② ❝♦♥❞✐t✐♦♥s ✐s ❡q✉✐✈❛❧❡♥t t♦ t❤❡ ❛♣♣❧✐❝❛t✐♦♥ ♦❢ ❛ ❡①t❡r♥❛❧ ✜❡❧❞✳
❋✐♥❛❧❧②✱ ✐t ✇❛s st✉❞✐❡❞ t❤❡ ❝r❡❛t✐♦♥ ♦❢ ♣❛rt✐❝❧❡s ✐♥ ❛ ❝♦s♠♦❧♦❣✐❝❛❧ ❝♦♥t❡①t✱ ❜❡✐♥❣ t❤❡ st❛t✐❝ ❝❛s❡ t❤❡ ❝r❡❛t✐♦♥ ♦❢ ♣❛rt✐❝❧❡s ✐♥ t❤❡ ✐♥✢❛t✐♦♥❛r② ❡♣♦❝❤ ♦❢ t❤❡ ✉♥✐✈❡rs❡✳ ❚❤❡ ❞②♥❛♠✐✲ ❝❛❧ ❝❛s❡ ❝♦rr❡s♣♦♥❞s t♦ t❤❡ r❡❤❡❛t✐♥❣ ♣❡r✐♦❞ ♦r✱ ♠♦r❡ ♣r❡❝✐s❡❧②✱ ✐ts ✐♥✐t✐❛❧ st❛❣❡ ❦♥♦✇♥ ❛s ♣r❡❤❡❛t✐♥❣✱ ✐♥ ✇❤✐❝❤ t❤❡ ❝r❡❛t✐♦♥ ♦❢ ♣❛rt✐❝❧❡s ✐s ♠♦r❡ ❡✣❝✐❡♥t✳ ❚❤❡ ❝r❡❛t✐♦♥ ♦❢ ♣❛rt✐❝❧❡s ✐♥ t❤❡ ✐♥✢❛t✐♦♥❛r② ❡♣♦❝❤ ♦❝❝✉rs ❞✉❡ t♦ t❤❡ ❛❝❝❡❧❡r❛t❡❞ ❡①♣❛♥s✐♦♥ ♦❢ t❤❡ ✉♥✐✈❡rs❡✳ ❇② ♠❡❛♥s ♦❢ ❛ s✐♠♣❧❡ ❝❛♥♦♥✐❝❛❧ tr❛♥s❢♦r♠❛t✐♦♥ ✐t ✇❛s ♣♦ss✐❜❧❡ t♦ ♦❜s❡r✈❡ t❤❛t t❤❡ ♠❡❝❤❛♥✐s♠ ♦❢ ♣❛rt✐❝❧❡ ❝r❡❛t✐♦♥ ✐♥ t❤✐s ♣❡r✐♦❞ ✐s t❤❡ s❛♠❡ ♦❢ t❤❡ ♦♥❡ ✐♥ ❙❝❤✇✐♥❣❡r ❡✛❡❝t✳ ■♥ t❤❡ s❛♠❡ ✇❛②✱ ❢♦r t❤❡ ♣r❡❤❡❛t✐♥❣✱ ✐♥ ✇❤✐❝❤ t❤❡ ♣❛rt✐❝❧❡ ❝r❡❛t✐♦♥ ✐s ❣✐✈❡♥ ❜② t❤❡ ♦s❝✐❧❧❛t✐♦♥ ♦❢ t❤❡ ✐♥✢❛t♦♥ ✜❡❧❞ ❛r♦✉♥❞ t❤❡ ♠✐♥✐♠✉♠ ♦❢ ✐ts ♣♦t❡♥t✐❛❧✱ t❤❡ ♠❡❝❤❛♥✐s♠ ♦❢ ❝r❡❛t✐♦♥ ❤❛♣♣❡♥s ❞✉❡ t♦ t❤❡ ♣❛r❛♠❡tr✐❝ r❡s♦♥❛♥❝❡ ❞❡s❝r✐❜❡❞ ❜② ❛ ▼❛t❤✐❡✉ ❡q✉❛t✐♦♥✳ ❚❤✐s ✐s ❡①❛❝t❧② t❤❡ s❛♠❡ ♠❡❝❤❛♥✐s♠ t❤❛t ❞❡s❝r✐❜❡s t❤❡ ♦s❝✐❧❧❛t♦r② ❙❝❤✇✐♥❣❡r ❡✛❡❝t✳
❊str✉t✉r❛ ❞❛ ❉✐ss❡rt❛çã♦
❆ ♣r❡s❡♥t❡ ❞✐ss❡rt❛çã♦ ♣r❡t❡♥❞❡ ❢❛③❡r ✉♠❛ ❛♥❛❧♦❣✐❛ ❡♥tr❡ ♠❡❝❛♥✐s♠♦s ❞❡ ❝r✐❛çã♦ ❞❡ ♣❛r✲ tí❝✉❧❛s ❝♦s♠♦❧ó❣✐❝♦s ❡ ♥❛ ❡❧❡tr♦❞✐♥â♠✐❝❛✳ ❉❡ss❛ ❢♦r♠❛✱ ♠♦str❛✲s❡ ♥❡❝❡ssár✐♦ ❛ ✐♥tr♦❞✉çã♦ ❞♦s ❝♦♥❝❡✐t♦s ❜ás✐❝♦s t❛♥t♦ ❞❡ ❝♦s♠♦❧♦❣✐❛✱ q✉❛♥t♦ ❞❡ t❡♦r✐❛ q✉â♥t✐❝❛ ❞❡ ❝❛♠♣♦s ❡ ❡❧❡✲ tr♦❞✐♥â♠✐❝❛✳ ❊ss❡s ❞♦✐s ú❧t✐♠♦s ❛♣❛r❡❝❡♠ ❝♦♥❢♦r♠❡ ♥❡❝❡ssár✐♦s ♥♦s ❝❛♣ít✉❧♦s ❡♠ q✉❡ ❡st✉❞❛♠♦s ♦s ❡❢❡✐t♦s ❞❡ ❝r✐❛çã♦ ❞❡ ♣❛rtí❝✉❧❛s ♥❛ ❡❧❡tr♦❞✐♥â♠✐❝❛✳ ❈♦♥t✉❞♦✱ ❝♦♠♦ ❡st❛ é ✉♠ ❞✐ss❡rt❛çã♦ ❞❛ ár❡❛ ❞❡ ❝♦s♠♦❧♦❣✐❛✱ ❛ ✐♥tr♦❞✉çã♦ ❞❡ s❡✉s ❝♦♥❝❡✐t♦s ❜ás✐❝♦s ❢♦✐ ❞❡t❛❧❤❛✲ ❞❛♠❡♥t❡ r❡✈✐s❛❞❛✳ ❈♦♠ ✐ss♦✱ ♦s ❈❛♣ít✉❧♦s ✷ ❡ ✸ ✭ ❡ ♦ ✐♥í❝✐♦ ❞♦ ❈❛♣ít✉❧♦ ✹✮ ♣♦❞❡♠ s❡r ♦♠✐t✐❞♦s ❞❛ ❧❡✐t✉r❛ ♣❛r❛ ❛q✉❡❧❡s q✉❡ ♦s t✐✈❡r❡♠ ❝♦♠♦ ♠❛tér✐❛ ❝♦♥❤❡❝✐❞❛✳
◆♦t❛çã♦
❆♣r❡s❡♥t❛♠♦s ❛q✉✐ ❛ ♥♦t❛çã♦ q✉❡ s❡rá ✉t✐❧✐③❛❞❛ ❛♦ ❧♦♥❣♦ ❞❛ ❞✐ss❡rt❛çã♦✳ Pr✐♠❡✐r❛♠❡♥t❡✱ ❞❡st❛❝❛♠♦s q✉❡ ✉t✐❧✐③❛r❡♠♦s ♦ s✐st❡♠❛ ❞❡ ✉♥✐❞❛❞❡s ♥♦ q✉❛❧ c=~=kB= 1✱ ❡♠ q✉❡ ❝ é ❛
✈❡❧♦❝✐❞❛❞❡ ❞❛ ❧✉③ ♥♦ ✈á❝✉♦ ❡kB é ❛ ❝♦♥st❛♥t❡ ❞❡ ❇♦❧t③♠❛♥♥✳ ❚❛♠❜é♠ t❡♠♦s q✉❡ í♥❞✐❝❡s ❣r❡❣♦s ✈❛r✐❛♠ ❞❡ ✵ ❛ ✸ ❡ í♥❞✐❝❡s ❧❛t✐♥♦s ✈❛r✐❛♠ ❞❡ ✶ ❛ ✸✳
❆❜❛✐①♦ ❛♣r❡s❡♥t❛♠♦s ♠❛✐s ❛❧❣✉♠❛s ♥♦t❛çõ❡s ✉t✐❧✐③❛❞❛s✳
●❡r❛❧
✯ ❝♦♠♣❧❡①♦ ❝♦♥❥✉❣❛❞♦
†ou h.c. ❍❡r♠✐t✐❛♥♦ ❝♦♥❥✉❣❛❞♦ ∂µou∂∂µou, µ ❉❡r✐✈❛❞❛ ♣❛r❝✐❛❧
Dµou ;µ ❉❡r✐✈❛❞❛ ❝♦✈❛r✐❛♥t❡
≡gµνD µDν
=DµDµ
❉✬▲❛♠❜❡rt✐❛♥♦
Re/Im P❛rt❡ r❡❛❧✴✐♠❛❣✐♥ár✐❛
❚r ❚r❛ç♦
[A, B] =AB−BA ❈♦♠✉t❛❞♦r
{A, B}=AB+BA ❆♥t✐❝♦♠✉t❛❞♦r
▼étr✐❝❛ ❞❡ ▼✐♥❦♦✇s❦✐✿
gµν =diag(1,−1,−1,−1) ▼❛tr✐③ γ✿
γµγν +γνγµ = 2gµν
γ5 =iγ0γ1γ2γ3
σµν = 2i [γµ, γν]
❈♦♥✈❡♥çã♦ ❞❡ s♦♠❛ ❞❡ ❊✐♥st❡✐♥✿
pq=pµqµ
❉✐str✐❜✉✐çõ❡s
❋✉♥çã♦ ❞❡❣r❛✉θ(x−y) =
0, se x < y
1, se x > y
❋✉♥çã♦ ❞❡❧t❛
δD(x−y) = 1 (2π)D
´
dDqeiq(x−y)
❉✐str✐❜✉✐çã♦ ❞❡ P❛✉❧✐✲❏♦r❞❛♥
△(x−y;m2)❂ −i
(2π)4 ´
❆❣r❛❞❡❝✐♠❡♥t♦s
❆❣r❛❞❡ç♦ ♣r✐♠❡✐r❛♠❡♥t❡ ❛♦ ♠❡✉ ♦r✐❡♥t❛❞♦r Pr♦❢✳ ❉r✳ ▲✉ís ❘❛✉❧ ❲❡❜❡r ❆❜r❛♠♦✱ ♣♦r t❡r ♠❡ ♦r✐❡♥t❛❞♦✱ ♣❡❧❛ ♣❛❝✐ê♥❝✐❛ ❡ ♣r✐♥❝✐♣❛❧♠❡♥t❡ ♣♦r ♠❡ ❡♥s✐♥❛r ❝♦♠♦ ❢❛③❡r ❝✐ê♥❝✐❛ ❝♦♠ q✉❛❧✐❞❛❞❡✱ ❡s❢♦rç♦ ❡ ❞❡❞✐❝❛çã♦✳ ❆❣r❛❞❡ç♦ t❛♠❜é♠ ❛♦ ❛♣♦✐♦ ❞♦s ❛❧✉♥♦s ❞❡ s❡✉ ❣r✉♣♦ ♣❡❧❛s ❝♦♥✈❡rs❛s✱ ❛❥✉❞❛s ❡ s❡♠✐♥ár✐♦s q✉❡ ❢♦r❛♠ s❡♠♣r❡ ♣r♦❞✉t✐✈♦s ❡ ♣r✐♥❝✐♣❛❧♠❡♥t❡ ❛♦ ❚❤✐❛❣♦ P❡r❡✐r❛ ♣♦r t❡r ❝♦♥tr✐❜✉í❞♦ ❝♦♠ ❞✐s❝✉ssõ❡s ♠✉✐t♦ r✐❝❛s s♦❜r❡ ♦ ❛ss✉♥t♦ ❞❡ss❛ ❞✐ss❡rt❛çã♦✳ ❆❣r❛❞❡ç♦ ✐♠❡♥s❛♠❡♥t❡ à ♠✐♥❤❛ ❢❛♠í❧✐❛✳ ❆♦s ♠❡✉s ♣❛✐s ❡ ✐r♠ã♦s q✉❡ s❡♠♣r❡ ❝♦♠♣r❡✲ ❡♥❞❡r❛♠ ❡ ❛♣♦✐❛r❛♠ ❛ ♠✐♥❤❛ ❛✉sê♥❝✐❛ s❛❜❡♥❞♦ q✉❡ ❡st❛✈❛ ❡♠ ❜✉s❝❛ ❞❡ ♠❡✉ s♦♥❤♦✳ ▼✉✐t♦ ♦❜r✐❣❛❞❛ ♣♦r t❡r❡♠ ❢❡✐t♦ t✉❞♦ s❡r ♣♦ssí✈❡❧✱ ♠❡ ❛♠❛❞♦ ❡ ❛♣♦✐❛❞♦ s❡♠♣r❡✳ ❆♠♦ ✈♦❝ês ❡ s✐♥t♦ ❝♦♠♦ s❡ ❡st✐✈❡ss❡ s❡♠♣r❡ ❛♦ ❧❛❞♦ ❞❡ ✈♦❝ês✳ ❆❣r❛❞❡ç♦ t❛♠❜é♠ ❛♦ ✈♦✈ô ❋❡rr❡✐r❛ ❡ ❛ ✈♦✈ó ❘♦s❛ q✉❡ ♠❡ tr❛t❛r❛♠ ❝♦♠♦ s✉❛ ✜❧❤❛ s❡♠♣r❡ ❡ ♠❡ ❛♣♦✐❛r❛♠ ♥❡ss❛ ❥♦r♥❛❞❛✳
❆❣r❛❞❡ç♦ ❛♦s ♠❡✉s ❛♠✐❣♦s ❞❡ ❣r❛❞✉❛çã♦ ❡ ❞❡ s❡♠♣r❡✿ ❇r✉♥♦✱ ❋❛❜✐♦✱ ❋❡❧✐♣❡✱ ❍❡r✲ ♠❛♥✱ ❏♦ã♦ ✭r❡❝❡♥t❡✱ ♠❛s s❡♠♣r❡ ♣r❡s❡♥t❡✮✱ P❡❞r♦✱ ❙✐❧❛s✱ ❚❤✐❛❣♦✱ ❲❛❧t❡r ❡ ❲✐❧❧✐❛♠✳ ▼❛s ❛❣r❛❞❡ç♦ ♣r✐♥❝✐♣❛❧♠❡♥t❡ ❛ ❊❞✉❛r❞♦ ❚♦s❤✐♦✱ ♠❡✉ ✐r♠ã♦ ❡ ❛♠✐❣♦ ✐♥❝♦♥❞✐❝✐♦♥❛❧✳
❆♦ ❉❡♣❛rt❛♠❡♥t♦ ❞❡ ❋ís✐❝❛ ▼❛t❡♠át✐❝❛ ❡ ❛ ❙✐♠♦♥❡ ❡ ❆♠é❧✐❛✳ P❡❧♦ ✜♥❛♥❝✐❛♠❡♥t♦ q✉❡ ♣♦ss✐❜✐❧✐t♦✉ ❡ss❛ ♣❡q✉✐s❛✱ ❛❣r❛❞❡ç♦ ❛♦ ❈◆Pq✳
❙✉♠ár✐♦
✶ ■♥tr♦❞✉çã♦ ✾
✷ ▼♦❞❡❧♦ ❈♦s♠♦❧ó❣✐❝♦ P❛❞rã♦ ✶✺
✷✳✶ Pr❡✈✐sõ❡s ❣❡♦♠étr✐❝❛s ❞♦ ▼❈P ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻ ✷✳✶✳✶ ❊str✉t✉r❛ ❞♦ ✉♥✐✈❡rs♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻ ✷✳✶✳✷ ❊①♣❛♥sã♦ ❞♦ ✉♥✐✈❡rs♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽ ✷✳✶✳✸ ❊✈♦❧✉çã♦ ❞♦ ✉♥✐✈❡rs♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶ ✷✳✶✳✹ ❍♦r✐③♦♥t❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺ ✷✳✷ ❉❡s❝r✐çã♦ ❞♦ ✉♥✐✈❡rs♦ ♣❡❧♦ ▼❈P ❡ ♦ ✉♥✐✈❡rs♦ ❥♦✈❡♠ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼ ✷✳✸ ❚❡st❡s ❞♦ ▼❈P ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵ ✷✳✸✳✶ ❆ ▲❡✐ ❞❡ ❍✉❜❜❧❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵ ✷✳✸✳✷ ❆❜✉♥❞â♥❝✐❛ ❞♦s ❊❧❡♠❡♥t♦s ▲❡✈❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶ ✷✳✸✳✸ ❆ ❘❛❞✐❛çã♦ ❈ós♠✐❝❛ ❞❡ ❋✉♥❞♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷ ✷✳✹ Pr♦❜❧❡♠❛s ❞♦ ▼❈P ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸ ✷✳✹✳✶ Pr♦❜❧❡♠❛ ❞❛ ♣❧❛♥✉r❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸ ✷✳✹✳✷ Pr♦❜❧❡♠❛ ❞♦ ❤♦r✐③♦♥t❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹ ✷✳✹✳✸ Pr♦❜❧❡♠❛ ❞❛ ♦r✐❣❡♠ ❞❛s ❡str✉t✉r❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✻ ✷✳✹✳✹ Pr♦❜❧❡♠❛ ❞♦s ♠♦♥♦♣♦❧♦s ♠❛❣♥ét✐❝♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✻
✸ ■♥✢❛çã♦ ✸✼
✸✳✶ ▼♦t✐✈❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽ ✸✳✶✳✶ Pr♦❜❧❡♠❛ ❞❛ ♣❧❛♥✉r❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵ ✸✳✶✳✷ Pr♦❜❧❡♠❛ ❞♦ ❤♦r✐③♦♥t❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶ ✸✳✶✳✸ Pr♦❜❧❡♠❛ ❞♦s ♠♦♥♦♣♦❧♦s ♠❛❣♥ét✐❝♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷ ✸✳✶✳✹ ❖ ♣r♦❜❧❡♠❛ ❞❛ ♦r✐❣❡♠ ❞❛s ❡str✉t✉r❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸ ✸✳✷ ❖ ♣❛r❛❞✐❣♠❛ ✐♥✢❛❝✐♦♥ár✐♦✿ ❛ ✐♥✢❛çã♦ ❡ ♦ ✐♥✢❛t♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸ ✸✳✷✳✶ ❘❡❣✐♠❡ ❞❡ r♦❧❛❣❡♠ ❧❡♥t❛ ✭❙❧♦✇✲❘♦❧❧✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✺ ✸✳✷✳✷ ◆ú♠❡r♦ ❞❡ ❡✲❢♦❧❞s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✼ ✸✳✷✳✸ ■♥✢❛çã♦ ❝❛ót✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽ ✸✳✸ Pré✲❛q✉❡❝✐♠❡♥t♦ ❡ ❘❡❛q✉❡❝✐♠❡♥t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✷ ✸✳✸✳✶ ❚❡♦r✐❛ ❊❧❡♠❡♥t❛r ❞♦ ❘❡❛q✉❡❝✐♠❡♥t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✹
✸✳✸✳✷ Pré✲❛q✉❡❝✐♠❡♥t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻
✹ ❚❡♦r✐❛ ❞❛s P❡rt✉r❜❛çõ❡s ❈♦s♠♦❧ó❣✐❝❛s ✺✽
✹✳✶ ❚❡♦r✐❛ ❈❧áss✐❝❛ ❞❛s P❡rt✉r❜❛çõ❡s ❈♦s♠♦❧ó❣✐❝❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾ ✹✳✶✳✶ ❚❡♦r✐❛ ❞❛s P❡rt✉r❜❛çõ❡s ♥❛ r❡❧❛t✐✈✐❞❛❞❡ ❣❡r❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾ ✹✳✷ ❚❡♦r✐❛ ◗✉â♥t✐❝❛ ❞❛s P❡rt✉r❜❛çõ❡s ❈♦s♠♦❧ó❣✐❝❛s✿ ✢✉t✉❛çõ❡s q✉â♥t✐❝❛s ❡ ♦
✧♥❛s❝✐♠❡♥t♦✧ ❞❛s ♣❡rt✉r❜❛çõ❡s ❝♦s♠♦❧ó❣✐❝❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✹ ✹✳✷✳✶ ◗✉❛♥t✐③❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✽ ✹✳✷✳✷ ❊s♣❡❝tr♦ ❞❡ P♦tê♥❝✐❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✸
✺ ❊❢❡✐t♦ ❙❝❤✇✐♥❣❡r ❊stát✐❝♦ ✽✼
✺✳✶ ❋♦r♠❛❧✐s♠♦ ❣❡r❛❧ ❡ q✉❛♥t✐③❛çã♦ ❝❛♥ô♥✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✾ ✺✳✷ ❊✈♦❧✉çã♦ ❚❡♠♣♦r❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✻ ✺✳✷✳✶ ❉✐♥â♠✐❝❛ ✈✐❛ t❡♦r✐❛ ❞❡ ❡s♣❛❧❤❛♠❡♥t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✼ ✺✳✷✳✷ ❉✐♥â♠✐❝❛ ✈✐❛ tr❛♥s❢♦r♠❛❞❛s ❞❡ ❇♦❣♦❧✐✉❜♦✈ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✻
✻ ❊❢❡✐t♦ ❙❝❤✇✐♥❣❡r ❉✐♥â♠✐❝♦ ✶✶✾
✻✳✶ ❊❢❡✐t♦ ❙❝❤✇✐♥❣❡r ❖s❝✐❧❛tór✐♦ ✈✐❛ t❡♦r✐❛ ❞❡ ❡s♣❛❧❤❛♠❡♥t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✷ ✻✳✶✳✶ ❚❡♥t❛t✐✈❛s ❡ ♣r♦♣♦st❛s ❡①♣❡r✐♠❡♥t❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✷ ✻✳✷ ❊❢❡✐t♦ ❙❝❤✇✐♥❣❡r ❖s❝✐❧❛tór✐♦ ✈✐❛ tr❛♥s❢♦r♠❛❞❛s ❞❡ ❇♦❣♦❧✐✉❜♦✈ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✸ ✻✳✷✳✶ ❋♦r♠❛❧✐s♠♦ ❞♦s ❡st❛❞♦s sq✉❡❡③❡❞ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✶ ✻✳✸ ❊❢❡✐t♦ ❈❛s✐♠✐r ❉✐♥â♠✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✷
✻✳✸✳✶ ◗✉❛♥t✐③❛çã♦ ❞♦ ❝❛♠♣♦ ❡s❝❛❧❛r ❡♠ ✶✰✶ ❞✐♠❡♥sõ❡s ❝♦♠ ❝♦♥❞✐çõ❡s ❞❡ ❝♦♥t♦r♥♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✹ ✻✳✸✳✷ ❖ ❝❛♠♣♦ ❡❧❡tr♦♠❛❣♥ét✐❝♦ ❡♠ ✉♠❛ ❝❛✈✐❞❛❞❡ ❞✐♥â♠✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✼ ✻✳✸✳✸ ❊①♣❡r✐♠❡♥t♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺✷
✼ ❆♥á❧♦❣♦s ❈♦s♠♦❧ó❣✐❝♦s ✶✺✼
✼✳✶ ❈r✐❛çã♦ ❞❡ P❛rtí❝✉❧❛s ♥❛ ■♥✢❛çã♦ ❡ ♦ ❊❢❡✐t♦ ❙❝❤✇✐♥❣❡r ❊stát✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺✽ ✼✳✶✳✶ ❈❛♠♣♦ ❊s❝❛❧❛r ▲✐✈r❡ ❡♠ ✉♠ ❊s♣❛ç♦✲❚❡♠♣♦ ❈✉r✈♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺✾ ✼✳✶✳✷ P❡rt✉r❜❛çõ❡s ✐♥✢❛❝✐♦♥ár✐❛s ❛ ❧❛ ❙❝❤✇✐♥❣❡r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻✶ ✼✳✷ ❈r✐❛çã♦ ❞❡ P❛rtí❝✉❧❛s ♥♦ Pré✲❛q✉❡❝✐♠❡♥t♦ ❡ ♦ ❊❢❡✐t♦ ❙❝❤✇✐♥❣❡r ❖s❝✐❧❛tór✐♦ ✶✻✽ ✼✳✷✳✶ Pré✲❛q✉❡❝✐♠❡♥t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻✽
✽ ❈♦♥❝❧✉sã♦ ✶✽✼
❆ ❉✐♥â♠✐❝❛ ✈✐❛ ❢♦r♠❛❧✐s♠♦ ❞❛ ▲❛❣r❛♥❣❡❛♥❛ ❡❢❡t✐✈❛ ✭♦✉ ❞❛ ❛çã♦ ❡❢❡t✐✈❛✮ ✶✾✽
❇ ■♥t❡❣r❛çã♦ ❝♦♠♣❧❡①❛ ✷✵✸
❈ ❋✉♥çõ❡s ❞❡ ❍❛♥❦❡❧ ✷✵✺
❈❛♣ít✉❧♦ ✶
■♥tr♦❞✉çã♦
❈♦s♠♦❧♦❣✐❛ é ♦ r❛♠♦ ❞❛ ❢ís✐❝❛ q✉❡ ❡st✉❞❛ ❛ ❡str✉t✉r❛✱ ❛ ❡①♣❛♥sã♦ ❡ ❛ ❡✈♦❧✉çã♦ ❞♦ ✉♥✐✈❡rs♦✱ ❞❡s❝r❡✈❡♥❞♦ ❞❡s❞❡ s✉❛ ♦r✐❣❡♠ ❛té s❡✉ ❢✉t✉r♦✳ ❈♦♠♦ ✉♠ r❛♠♦ ❞❛ ❝✐ê♥❝✐❛✱ ❡❧❛ ✉t✐❧✐③❛ ♦ ♠ét♦❞♦ ❝✐❡♥tí✜❝♦ ♣❛r❛ ❞❡s❝r❡✈❡r ♦ ✉♥✐✈❡rs♦ ❝♦♠♦ ✉♠ t♦❞♦✳ ■ss♦ q✉❡r ❞✐③❡r q✉❡ sã♦ ❢❡✐t❛s t❡♦r✐❛s ❡ ❤✐♣ót❡s❡s q✉❡ ♣♦❞❡♠ s❡r t❡st❛❞❛s ♣♦r ♦❜s❡r✈❛çõ❡s ♦✉ ❡①♣❡r✐♠❡♥t♦s✳ ❆í r❡s✐❞❡ ♦ ♠❛✐♦r ❞❡s❛✜♦ ❞❛ ❝♦s♠♦❧♦❣✐❛✱ q✉❡ r❡t❛r❞♦✉ s✉❛ ❛❝❡✐t❛çã♦ ❝♦♠♦ ❝✐ê♥❝✐❛✳ ❈♦♠♦ ♦ ✉♥✐✈❡rs♦ é ✉♠ ♦❜❥❡t♦ q✉❡ ♥ã♦ ♣♦❞❡ s❡r r❡♣r♦❞✉③✐❞♦ ❡♠ ❧❛❜♦r❛tór✐♦✱ ❛ ❝♦s♠♦❧♦❣✐❛ ♥❡❝❡ss✐t❛ ❞❡ ❛rt✐❢í❝✐♦s ♣❛r❛ ♣♦❞❡r ❝♦♥st❛t❛r s✉❛s ♣r❡✈✐sõ❡s✳ P❛r❛ ✐ss♦ sã♦ ✉t✐❧✐③❛❞❛s ♦❜s❡r✈❛çõ❡s ❞❡ s✉❛s ❡str✉t✉r❛s ✈✐sí✈❡✐s ❡ ♠❡❞✐çõ❡s ✐♥❞✐r❡t❛s ❞❡ ❢❡♥ô♠❡♥♦s q✉❡ sã♦ ✜s✐❝❛♠❡♥t❡ ❛ss♦❝✐❛❞♦s ❛ ❛❝♦♥t❡❝✐♠❡♥t♦s ♦❝♦rr✐❞♦s ♥♦ ✉♥✐✈❡rs♦✳ ❆❧t❡r♥❛t✐✈❛♠❡♥t❡✱ ❢❛③❡♠♦s t❛♠❜é♠ ♦ ✉s♦ ❞❡ ❛♥❛❧♦❣✐❛s ❞❡ s✐st❡♠❛s ❝♦s♠♦❧ó❣✐❝♦s ❝♦♠ s✐st❡♠❛s q✉❡ sã♦ ❝♦♥❤❡❝✐❞♦s ❡ r❡♣r♦❞✉tí✈❡✐s ♥❛ ❚❡rr❛✳ ◆❡ss❛ ❞✐ss❡rt❛çã♦ ✉t✐❧✐③❛r❡♠♦s ❛♥❛❧♦❣✐❛s ♣❛r❛ ❛ ❞❡s❝r✐çã♦ ❞♦ ♠♦❞❡❧♦ ❝♦s♠♦❧ó❣✐❝♦ ❞❡ ❝r✐❛çã♦ ❞❡ ♣❛rtí❝✉❧❛s ❞✉r❛♥t❡ ♦ ♣❡rí♦❞♦ ✐♥✢❛❝✐♦♥ár✐♦ ❡ ❞♦ r❡❛q✉❡❝✐♠❡♥t♦✳
❆ ❡r❛ ❞❛ ❝♦s♠♦❧♦❣✐❛ ♠♦❞❡r♥❛ t❡✈❡ ✐♥í❝✐♦ ♥♦ ❝♦♠❡ç♦ ❞♦ sé❝✉❧♦ ❳❳✱ ❝♦♠ ♦s tr❛❜❛❧❤♦s s❡♠✐♥❛✐s ❞❡ ❆❧❜❡rt ❊✐♥st❡✐♥✳ ❋♦✐ ♣♦ssí✈❡❧✱ ❝♦♠ ♦ ❛❞✈❡♥t♦ ❞❛ t❡♦r✐❛ ❞❛ r❡❧❛t✐✈✐❞❛❞❡✱ ❞❡s❝r❡✲ ✈❡r ♦ ♣r✐♠❡✐r♦ ♠♦❞❡❧♦ ♠❛t❡♠át✐❝♦ ❞♦ ✉♥✐✈❡rs♦✱ ❢❡✐t♦ ♣♦r ❡❧❡ ❡♠ ✶✾✶✼ ❬✶✱ ✷❪✳ ◆❡ss❡ ♠♦❞❡❧♦ tí♥❤❛♠♦s ✉♠ ✉♥✐✈❡rs♦ ❡stát✐❝♦ ❡ ✐♥✜♥✐t♦✳ P♦st❡r✐♦r♠❡♥t❡✱ ❆✳ ❋r✐❡❞♠❛♥♥ ❡ ❲✳ ❞❡ ❙✐tt❡r ✭s❡❣✉✐❞♦s✱ ❞❡♣♦✐s✱ ♣♦r ●✳ ▲❡♠❛îtr❡✱ ❍✳ ❘♦❜❡rts♦♥ ❡ ❆✳ ❲❛❧❦❡r✮✱ ❜❛s❡❛❞♦s ♥❛s ❡q✉❛çõ❡s ❞❡ ❊✐♥st❡✐♥✱ ♠♦str❛r❛♠ q✉❡ ♠♦❞❡❧♦s ❞♦ ✉♥✐✈❡rs♦ ♥ã♦✲❡stát✐❝♦s ❡r❛♠ t❛♠❜é♠ ♣♦ssí✈❡✐s✳
▼❛s ❢♦✐ ❝♦♠ ❊✳ ❍✉❜❜❧❡✱ ❡♠ ✶✾✷✾ ❬✸❪✱ q✉❡ s❡ t❡✈❡ ❛ ♣r✐♠❡✐r❛ ♣r♦✈❛ ❡♠♣ír✐❝❛ ❞❡ q✉❡ ♦ ✉♥✐✈❡rs♦ ❡st❛✈❛ ❡♠ ❡①♣❛♥sã♦ ❡ ❡ss❛ ❡①♣❛♥sã♦ ❡r❛ ❝♦♠♣❛tí✈❡❧ ❝♦♠ ❛ r❡❧❛t✐✈✐❞❛❞❡ ❣❡r❛❧✳ ❈♦♠ ❡ss❛s ✐❞é✐❛s ❡♠ ♠ã♦s✱ ●❡♦r❣❡ ●❛♠♦✇ ❬✺❪ ❡♠ ✶✾✹✽ ❡ s❡✉s ❛❧✉♥♦s ❘❛❧♣❤ ❆❧♣❤❡r ❡ ❘♦❜❡rt ❍❡r♠❛♥ ❬✹✱ ✻❪ ❡♠ ✶✾✺✵ ♣r❡✈✐r❛♠ ❛ ❘❛❞✐❛çã♦ ❈ós♠✐❝❛ ❞❡ ❋✉♥❞♦ ✭❘❈❋✮✱ ❞❡s❝♦✲ ❜❡rt❛ ❡♠ ✶✾✻✺ ♣♦r ❆r♥♦❧❞ ❆✳ P❡♥③✐❛s ❡ ❘♦❜❡rt ❲✳ ❲✐❧s♦♥ ❬✼❪✱ ♦ q✉❡ ❧❤❡s r❡♥❞❡✉ ♦ ♣rê♠✐♦ ◆♦❜❡❧✳ ❉❡ss❛ ❢♦r♠❛✱ ❛ ❝♦s♠♦❧♦❣✐❛ ❥á r❡✉♥✐❛ ♣r♦✈❛s ❜❛st❛♥t❡ ❝♦♥t✉♥❞❡♥t❡s ❞❡ ✉♠ ✉♥✐✈❡rs♦ ❞✐♥â♠✐❝♦ ❡ ❡♠ ❡①♣❛♥sã♦✱ ♦ q✉❡ s✐❣♥✐✜❝❛✈❛ ✉♠❛ r✉♣t✉r❛ ❞♦ ♣❡♥s❛♠❡♥t♦ t✐❞♦ ❝♦♠♦ ❞❡✜♥✐✲ t✐✈♦ ♣❡❧❛ ❤✉♠❛♥✐❞❛❞❡✱ ❛q✉❡❧❡ ❞❡ ✉♠ ✉♥✐✈❡rs♦ ❡stát✐❝♦ ❡ ✐♥✜♥✐t♦✳ ■ss♦ ♣❡r♠✐t✐❛ ❝♦♥❝❡❜❡r q✉❡✱ ♥♦ ♣❛ss❛❞♦✱ ♦ ✉♥✐✈❡rs♦ ❡r❛ ♠✉✐t♦ ♠❡♥♦r ❡ ♠❛✐s q✉❡♥t❡ ❡✱ ❥✉♥t❛♠❡♥t❡ ❝♦♠ ❛ ❤✐♣ót❡s❡ ❞❡ ❤♦♠♦❣❡♥❡✐❞❛❞❡ ❡ ✐s♦tr♦♣✐❛✱ ❢♦✐ ❝♦♥str✉í❞♦ ♦ ▼♦❞❡❧♦ ❈♦s♠♦❧ó❣✐❝♦ P❛❞rã♦✱ ♦✉ ▼♦❞❡❧♦
❞♦ ❇✐❣ ❇❛♥❣ ◗✉❡♥t❡✳ ❊ss❛s ❞❡s❝♦❜❡rt❛s ❝♦❧♦❝❛✈❛♠✱ ❛ss✐♠✱ ❛ ❝♦s♠♦❧♦❣✐❛ ♠❛✐s ♣❡rt♦ ❞♦ r✐❣♦r ❝✐❡♥tí✜❝♦ ❡s♣❡r❛❞♦ ♣♦r ✉♠❛ ❝✐ê♥❝✐❛ ❢ís✐❝❛✱ ❡♠ q✉❡ ❛s ♣r❡✈✐sõ❡s ❡r❛♠ ❢❡✐t❛s ❡ ❝❤❡❝❛✲ ❞❛s ❡①♣❡r✐♠❡♥t❛❧♠❡♥t❡✳ ▼❡s♠♦ ❝♦♠ ❡ss❡s ❛✈❛♥ç♦s✱ ♥♦s ❛♥♦s ✶✾✼✵ ❛✐♥❞❛ ❤❛✈✐❛ r❡✈✐st❛s ❝✐❡♥tí✜❝❛s ❝♦♠♦ ❛ ❛❧❡♠ã ❩❡✐ts❝❤r✐❢t ❢ür P❤②s✐❦ ✭❏♦r♥❛❧ ❞❡ ❋ís✐❝❛✮✱ q✉❡ s✐♠♣❧❡s♠❡♥t❡ ♥ã♦ ❛❝❡✐t❛✈❛♠ q✉❛✐sq✉❡r ❛rt✐❣♦s ❝♦♠ ♦ t❡♠❛ ❝♦s♠♦❧♦❣✐❛✳ ❈♦♥t✉❞♦✱ ♥♦s ✶✾✽✵✱ ✐♥✐❝✐♦✉✲s❡ ♦ q✉❡ ❝❤❛♠❛♠♦s ❞❡ ❡r❛ ❞❛ ❝♦s♠♦❧♦❣✐❛ ❞❡ ♣r❡❝✐sã♦✱ ❝♦♠ ♦ ❧❛♥ç❛♠❡♥t♦ ❞♦ s❛té❧✐t❡ ❈❖❇❊ ❬✽✱ ✾❪✱ ❡♠ q✉❡ ♦s ❞❛❞♦s ♦❜t✐❞♦s ♦st❡♥t❛✈❛♠ ✉♠❛ ♣r❡❝✐sã♦ ♠✉✐t♦ ❣r❛♥❞❡✱ ❛❧é♠ ❞❡ ✉♠❛ ❡st❛tíst✐❝❛ ♠✉✐t♦ ❜♦❛✳ ▼❛✐s r❡❝❡♥t❡♠❡♥t❡✱ ♥♦s ú❧t✐♠♦s ✺ ❛♥♦s✱ ♦ s❛té❧✐t❡ ❲▼❆P ❬✷✶✱ ✷✷✱ ✷✸❪ ❛✉♠❡♥✲ t♦✉ ❝♦♥s✐❞❡r❛✈❡❧♠❡♥t❡ ❛ q✉❛❧✐❞❛❞❡ ❞♦s ❞❛❞♦s ♦❜t✐❞♦s✱ ❝♦❧♦❝❛♥❞♦✲♥♦s ♥❛ ❡r❛ ❞❛ ❝♦s♠♦❧♦❣✐❛ ❞❡ ❛❧t❛ ♣r❡❝✐sã♦✳
❖s r❡s✉❧t❛❞♦s ❞❡ss❡s ú❧t✐♠♦s ❛♥♦s ❞❛ ❝♦s♠♦❧♦❣✐❛ ♠♦❞❡r♥❛ ♣❡r♠✐t✐r❛♠✲♥♦s ❝♦♥str✉✐r ✉♠ ♠♦❞❡❧♦ ♣❛r❛ ♦ ✉♥✐✈❡rs♦✿ ♦ ♠♦❞❡❧♦ ❝♦s♠♦❧ó❣✐❝♦ ♣❛❞rã♦ ❬✸✶✱ ✷✾✱ ✸✵✱ ✸✷❪✳ ❊❧❡ ♣r❡✈ê ✉♠ ✉♥✐✈❡rs♦ ❤♦♠♦❣ê♥❡♦ ❡ ✐s♦tró♣✐❝♦ ❡♠ ❧❛r❣❛s ❡s❝❛❧❛s ❝♦♠ ✶✸✱✾ ❜✐❧❤õ❡s ❞❡ ❛♥♦s✱ ♣r❛t✐❝❛♠❡♥t❡ ♣❧❛♥♦✱ ♣❡r♠❡❛❞♦ ♣♦r ✉♠❛ r❛❞✐❛çã♦ ❡❧❡tr♦♠❛❣♥ét✐❝❛ ❞❡ t❡♠♣❡r❛t✉r❛ ❞❡ ❛♣r♦①✐♠❛❞❛♠❡♥t❡ ✷✱✼✺ ❑ ❡ ❝♦♠♣♦st♦ ♣♦r ❛♣r♦①✐♠❛❞❛♠❡♥t❡ ✹✪ ❞❡ ♠❛tér✐❛ ❝♦♠✉♠✱ ✵✱✵✶✪ ❞❡ r❛❞✐❛çã♦✱ ✷✸✪ ❞❡ ♠❛tér✐❛ ❡s❝✉r❛ ❡ ✼✸✪ ❞❡ ❡♥❡r❣✐❛ ❡s❝✉r❛ ❬✷✹❪✳ ❖s ❡①♣❡r✐♠❡♥t♦s r❡❝❡♥t❡s ❝♦♥✜r♠❛r❛♠ ♠✉✐t❛s ❞❛s ❤✐♣ót❡s❡s ❞❡s❝r✐t❛s ♥❡ss❡ ♠♦❞❡❧♦✱ ♠❛s t❛♠❜é♠ ♥♦s ♣❡r♠✐t✐r❛♠ ✈❡r✐✜❝❛r ❞❡s✈✐♦s ❡♠ ❛❧❣✉♠❛s ❞❡❧❛s✳ ❆ ❤♦♠♦❣❡♥❡✐❞❛❞❡ ❡ ✐s♦tr♦♣✐❛ ❞♦ ✉♥✐✈❡rs♦ sã♦ ❝♦♥✜r♠❛❞❛s ♣♦r ♠❡✐♦ ❞❛ ❛♥á❧✐s❡ ❞❛ ❘❈❋✳ ❈♦♥t✉❞♦✱ ❝♦♠ ♦s ❞❛❞♦s ❝♦❧❤✐❞♦s ♣❡❧♦ s❛té❧✐t❡ ❲▼❆P✱ ❢♦✐ ♣♦ssí✈❡❧ ❞❡t❡r♠✐♥❛r ✉♠ ❞❡s✈✐♦ ❞❡ ✵✱✵✵✶✪ ♥❛ t❡♠♣❡r❛t✉r❛ ❞❛ r❛❞✐❛çã♦ ❡♠ ❞✐❢❡r❡♥t❡s ❞✐r❡çõ❡s ❬✷✹❪✳ ■ss♦ ✐♥❞✐❝❛ ✢✉t✉❛çõ❡s ✐♥✐❝✐❛✐s q✉❛♥❞♦ ♦ ✉♥✐✈❡rs♦ ❡r❛ ♠❛✐s ❥♦✈❡♠✱ s❡♠❡♥t❡s ♣❛r❛ ❛ ❢♦r♠❛çã♦ ❞❛s ❡str✉t✉r❛s ❡♠ ❧❛r❣❛ ❡s❝❛❧❛ q✉❡ t❡♠♦s ❤♦❥❡ ❡♠ ❞✐❛✳ P♦❞❡♠♦s ♣❡♥s❛r t❛♠❜é♠ ♣♦r q✉❡ ♦ ✉♥✐✈❡rs♦ é tã♦ ❤♦♠♦❣ê♥❡♦ ❡ ✐s♦tró♣✐❝♦✱ s❡♥❞♦ q✉❡ r❡❣✐õ❡s q✉❡ ♥ã♦ sã♦ ❧✐❣❛❞❛s ❝❛✉s❛❧♠❡♥t❡ tê♠ ❛ ♠❡s♠❛ t❡♠♣❡r❛t✉r❛ ♥❛ ❘❈❋✳ ❖✉ ♣♦❞❡♠♦s ♣❡♥s❛r ❛✐♥❞❛ ♣♦r q✉❡ ♦ ✉♥✐✈❡rs♦ é tã♦ ♣❧❛♥♦✳ ❚♦❞❛s ❡ss❛s q✉❡stõ❡s ✭❡ ♦✉tr❛s✮ ♥ã♦ sã♦ ❡①♣❧✐❝❛❞❛s ♣❡❧♦ ♠♦❞❡❧♦ ❝♦s♠♦❧ó❣✐❝♦ ♣❛❞rã♦✳ ❈♦♠ ♦ ✐♥t✉✐t♦ ❞❡ r❡s♦❧✈❡r ❡ss❡s ✧♣r♦❜❧❡♠❛s✧ ❞♦ ♠♦❞❡❧♦ ❞♦ ✉♥✐✈❡rs♦✱ s✉r❣✐✉✱ ❡♠ ✶✾✽✶✱ ❞❡s❡♥✈♦❧✈✐❞❛ ♣♦r ❆❧❛♥ ●✉t❤ ❬✶✵❪ ✭ ❡ ❞❡ ♠❛♥❡✐r❛ ❞✐❢❡r❡♥t❡ ♣♦r ❙t❛r♦❜✐♥s❦② ❬✶✶❪✮✱ ❛ t❡♦r✐❛ ❞❛ ✐♥✢❛çã♦✳ ❊ss❛ t❡♦r✐❛ s✉r❣❡ ♣❛r❛ s♦❧✉❝✐♦♥❛r ♦ ♣r♦❜❧❡♠❛ ❞❛s ❝♦♥❞✐çõ❡s ✐♥✐❝✐❛✐s ❞♦ ✉♥✐✈❡rs♦✳ ❊❧❛ ♣r❡✈ê ✉♠ ♣❡rí♦❞♦ ❞❡ ❡①♣❛♥sã♦ ❡①♣♦♥❡♥❝✐❛❧ ❡♠ s❡✉s ❡stá❣✐♦s ✐♥✐❝✐❛✐s q✉❡ s❡r✐❛ ❝❛♣❛③ ♥ã♦ ❛♣❡♥❛s ❞❡ ❣❡r❛r ❛s ✐♥♦♠♦❣❡♥❡✐❞❛❞❡s ♣r✐♠♦r❞✐❛✐s✱ ❝♦♠♦ t❛♠❜é♠ ❝♦♥❡❝t❛r ❝❛✉s❛❧♠❡♥t❡ r❡❣✐õ❡s ❞♦ ✉♥✐✈❡rs♦ ❛♥t❡s ❞❛ ✐♥✢❛çã♦✳ ❚❛♠❜é♠ ♣♦❞❡♠♦s ♣❡♥s❛r q✉❡ ❡ss❛ ❡①♣❛♥sã♦ ❞❡✐①❛ ♦ ✉♥✐✈❡rs♦ ❡♥♦r♠❡♠❡♥t❡ ❣r❛♥❞❡ ❛♣ós ❡ss❡ ♣❡rí♦❞♦✱ ❢❛③❡♥❞♦ ❝♦♠ q✉❡ ♣❛r❡ç❛ ♣❧❛♥♦✳ ❆ ✐♥✢❛çã♦ r❡s♦❧✈❡ ❛✐♥❞❛ ♦ ♣r♦❜❧❡♠❛ ❞❛ ❢♦r♠❛çã♦ ❞❛s ❡str✉t✉r❛s ❝♦s♠♦❧ó❣✐❝❛s✱ ❢♦r♠❛❞❛s ♣♦r ♠❡✐♦ ❞♦ ❝♦❧❛♣s♦ ❣r❛✈✐t❛❝✐♦♥❛❧✱ ❛ ♣❛rt✐r ❞❛s ✢✉t✉❛çõ❡s ♣r✐♠♦r❞✐❛✐s ❣❡r❛❞❛s ♥❡ss❡ ♣❡rí♦❞♦✳ ❆ ✐♥✢❛çã♦ ♣♦❞❡ s❡r ❞❡s❝r✐t❛ ❝♦♠♦ ♠♦✈✐❞❛ ♣♦r ✉♠ ❝❛♠♣♦ ❡s❝❛❧❛r ❝❤❛♠❛❞♦ ✐♥✢❛t♦♥✳ ❉✉r❛♥t❡ ❡ss❡ ♣❡rí♦❞♦ ❡ss❡ ❝❛♠♣♦ r♦❧❛ ❧❡♥t❛♠❡♥t❡ ❛té ♦ ♠í♥✐♠♦ ❞❡ s❡✉ ♣♦t❡♥❝✐❛❧✳ ❊ss❡ ♠❡❝❛♥✐s♠♦ q✉❡ ♣r♦❞✉③ ❛s ♣❡rt✉r❜❛çõ❡s ♣r✐♠♦r❞✐❛✐s ♦❝♦rr❡ ❞❡✈✐❞♦ às ✢✉t✉❛çõ❡s q✉â♥t✐❝❛s ❞♦ ✈á❝✉♦✱ q✉❡ s✐❣♥✐✜❝❛ q✉❡ ♣❛r❡s ✈✐rt✉❛✐s ❞❡ ♣❛rtí❝✉❧❛s ❡ ❛♥t✐♣❛rtí❝✉❧❛s sã♦ ❝r✐❛❞❛s ❡ ❛♥✐q✉✐❧❛❞❛s ❝♦♥t✐♥✉❛♠❡♥t❡ ♥♦ ✈á❝✉♦✳ ❈♦♠ ❛ ❡①♣❛♥sã♦ ❛❝❡❧❡r❛❞❛ ❞♦ ✉♥✐✈❡rs♦✱ ♥♦ ♣❡rí♦❞♦
✐♥✢❛❝✐♦♥ár✐♦✱ ❡ss❡s ♣❛r❡s ✈✐rt✉❛✐s s❡ ❞✐st❛♥❝✐❛♠ ♠✉✐t♦ ✉♥s ❞♦s ♦✉tr♦s✱ ❞✐ss♦❝✐❛♥❞♦✲s❡ ❡ ❝r✐❛♥❞♦ ✉♠ ♣❛r ❞❡ ♣❛rtí❝✉❧❛s r❡❛✐s✳ ❆ss✐♠✱ ❛ ✐♥✢❛çã♦ ♦❢❡r❡❝❡ ✉♠ ♠❡❝❛♥✐s♠♦ ❡♠ q✉❡ é ♣♦ssí✈❡❧ ❝r✐❛r ♠❛tér✐❛ ❞♦ ✈á❝✉♦✳ ■ss♦ ❢❛③ ❝♦♠ q✉❡ ❡ss❛ t❡♦r✐❛ s❡❥❛ ♠✉✐t♦ ❡s♣❡❝✐❛❧✱ s❡♥❞♦ ❝❛♣❛③ ❞❡ ❝♦♠❜✐♥❛r ❛ ♠❡❝â♥✐❝❛ q✉â♥t✐❝❛ ❝♦♠ ❛ r❡❧❛t✐✈✐❞❛❞❡ ❣❡r❛❧✳
❉❡ss❛ ❢♦r♠❛✱ ❛ ✐♥✢❛çã♦ é r❡s♣♦♥sá✈❡❧ ♣❡❧❛ ♦r✐❣❡♠ ❞❛s ♣❡rt✉r❜❛çõ❡s ✐♥✐❝✐❛✐s✳ ❊ss❛s ♣❡rt✉r❜❛çõ❡s ❞♦ ❝❛♠♣♦ q✉â♥t✐❝♦ ❡s❝❛❧❛r sã♦ ❣❡r❛❞❛s ❡♠ t♦❞♦s ♦s ✐♥st❛♥t❡s ❞❛ ✐♥✢❛çã♦ ❡ ❝♦♠ ❞✐❢❡r❡♥t❡s ❝✉♠♣r✐♠❡♥t♦s ❞❡ ♦♥❞❛✳ ❊❧❛s sã♦ ❣❡r❛❞❛s ❡ s❡ ✧❡st✐❝❛♠✧ ✭s❡✉ ❝♦♠♣r✐♠❡♥t♦ ❞❡ ♦♥❞❛ ❝r❡s❝❡✮ ❞✉r❛♥t❡ ❛ ✐♥✢❛çã♦✳ ❆s ♣❡rt✉r❜❛çõ❡s q✉❡ ❛t✐♥❣❡♠ ❝♦♠♣r✐♠❡♥t♦s ❞❡ ♦♥❞❛ ♠❛✐♦r❡s q✉❡ ♦ r❛✐♦ ❞❡ ❍✉❜❜❧❡ ❞♦ ✉♥✐✈❡rs♦ ♣❡r♠❛♥❡❝❡♠ ❝♦♥❣❡❧❛❞❛s ❛té ♦ ♠♦♠❡♥t♦ ❡♠ q✉❡ ♦ ✉♥✐✈❡rs♦ s❡ ❡①♣❛♥❞❛ ♦ s✉✜❝✐❡♥t❡ ❡ ❡♥❣❧♦❜❡✲❛s ❡♠ s❡✉ ❤♦r✐③♦♥t❡ ❝❛✉s❛❧✳ ❈♦♠ ✐ss♦✱ t♦❞❛s ❛s ♣❡rt✉r❜❛çõ❡s✱ ♥♦ ✜♠ ❞❛ ✐♥✢❛çã♦✱ tê♠ ❡ss❡♥❝✐❛❧♠❡♥t❡ ❛ ♠❡s♠❛ ❛♠♣❧✐t✉❞❡✳ P♦❞❡♠♦s✱ ❞❡ ♠❛♥❡✐r❛ ❛♥á❧♦❣❛✱ ♣❡♥s❛r q✉❡ ❛ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❡ ❝r✐❛çã♦ ❞❡ ♣❛rtí❝✉❧❛s ♥❛ ✐♥✢❛çã♦ é ♣r❛t✐❝❛♠❡♥t❡ ❛ ♠❡s♠❛ ❡♠ t♦❞♦s ♦s ♣♦♥t♦s ❞♦ ✉♥✐✈❡rs♦✳ ❈♦♠♦ ❛ ❡①♣❛♥sã♦ ❛❝❡❧❡r❛❞❛ é q✉❛s❡ ❝♦♥st❛♥t❡ ❡♠ t♦❞♦ ♦ ❡s♣❛ç♦✱ ❛ q✉❛♥t✐❞❛❞❡ ❞❡ ♣❛rtí❝✉❧❛s ❝r✐❛❞❛s ♣♦r ✉♥✐❞❛❞❡ ❞❡ ✈♦❧✉♠❡ ❡ ♣♦r ✉♥✐❞❛❞❡ ❞❡ t❡♠♣♦ s❡rá t❛♠❜é♠ ❝♦♥st❛♥t❡✳ ❆ss✐♠✱ ♦ ♣❛❞rã♦ ❞❡ss❛s ♣❡rt✉r❜❛çõ❡s ❞❡ ❞❡♥s✐❞❛❞❡ ❞❡✈❡ ♠❛♥t❡r✲s❡ ❛♦ ❧♦♥❣♦ ❞❛ ✐♥✢❛çã♦ ❡✱ ❝♦♠ ✐ss♦✱ ❡❧❛s tê♠ q✉❛s❡ ❛ ♠❡s♠❛ ❛♠♣❧✐t✉❞❡ ❡♠ q✉❛✐sq✉❡r ❡s❝❛❧❛s✳ ❊ss❡ ❡s♣❡❝tr♦ ✐♥✈❛r✐❛♥t❡ ❞❡ ❡s❝❛❧❛ ♣♦❞❡ s❡r ♠❡❞✐❞♦ ♥❛ ❘❈❋ ❡ é ✉♠❛ ✐♠♣♦rt❛♥t❡ ✈❡r✐✜❝❛çã♦ ♣❛r❛ ❡ss❡ ♠❡❝❛♥✐s♠♦ ❞❡ ❣❡r❛çã♦ ❞❡ ♣❡rt✉r❜❛çõ❡s ❡ ♣❛r❛ ❛ t❡♦r✐❛ ❞❛ ✐♥✢❛çã♦ ❬✷✹❪✳
❆♦ ✜♠ ❞❛ ✐♥✢❛çã♦✱ q✉❛♥❞♦ ♦ ❝❛♠♣♦ ❡s❝❛❧❛r t❡r♠✐♥❛ ❞❡ r♦❧❛r ❧❡♥t❛♠❡♥t❡ ❡♠ ❞✐r❡çã♦ ❛♦ ♠í♥✐♠♦ ❞❡ s❡✉ ♣♦t❡♥❝✐❛❧ ❡❢❡t✐✈♦✱ ❡❧❡ ♣❛ss❛ ❛ ♦s❝✐❧❛r r❛♣✐❞❛♠❡♥t❡ ❡♠ t♦r♥♦ ❞❡ss❡ ♠í♥✐♠♦✳ ❈♦♥❢♦r♠❡ ✈❛✐ ♦s❝✐❧❛♥❞♦✱ ♦ ❝❛♠♣♦✱ s❡ ❡st✐✈❡r ❛❝♦♣❧❛❞♦ ❛ ♦✉tr♦s ❝❛♠♣♦s ❞❡ ♠❛tér✐❛✱ ♣❡r❞❡ ❡♥❡r❣✐❛ ♣♦r ♠❡✐♦ ❞❛ ❝r✐❛çã♦ ❞❡ ♣❛rtí❝✉❧❛s✱ ❛té ❛t✐♥❣✐r ♦ ♠í♥✐♠♦ ❞♦ ♣♦t❡♥❝✐❛❧✳ ◗✉❛s❡ t♦❞❛ ❛ ♠❛tér✐❛ q✉❡ ❝♦♥st✐t✉✐ ♦ ✉♥✐✈❡rs♦ é ❝r✐❛❞❛ ❞✉r❛♥t❡ ❡ss❛ ❢❛s❡✱ ❝❤❛♠❛❞❛ ❞❡ r❡❛q✉❡❝✐♠❡♥t♦✳ ❊ss❡ ♥♦♠❡ é ❞❛❞♦ ♣♦rq✉❡ t♦❞❛s ❡ss❛s ♣❛rtí❝✉❧❛s ❝r✐❛❞❛s ✐♥t❡r❛❣❡♠ ❡♥tr❡ s✐ ❡ ❛t✐♥❣❡♠ ✉♠ ❡st❛❞♦ ❞❡ ❡q✉✐❧í❜r✐♦ tér♠✐❝♦ ❝♦♠ t❡♠♣❡r❛t✉r❛ ✜♥❛❧ Treaq✳ ❊ss❡ ♠❡❝❛♥✐s♠♦ ❞❡ ❝r✐❛çã♦ ❞❡
♣❛rtí❝✉❧❛s s♦♠❡♥t❡ é ❡✜❝✐❡♥t❡✱ ♦✉ s❡❥❛✱ ❝r✐❛ ✉♠❛ q✉❛♥t✐❞❛❞❡ ❣r❛♥❞❡ ❞❡ ♣❛rtí❝✉❧❛s✱ q✉❛♥❞♦ t❡♠♦s ♦ r❡❣✐♠❡ ❞❡ r❡ss♦♥â♥❝✐❛ ♣❛r❛♠étr✐❝❛✱ q✉❛♥❞♦ ❛ ❛♠♣❧✐t✉❞❡ ❞❛s ♦s❝✐❧❛çõ❡s ❞♦ ❝❛♠♣♦ ❡♠ t♦r♥♦ ❞♦ ♠í♥✐♠♦ sã♦ ❛♠♣❧❛s✳ ❊ss❡ ❡stá❣✐♦ ❞❡ ❞❡❝❛✐♠❡♥t♦ rá♣✐❞♦ ❡ ♥ã♦ ♣❡rt✉r❜❛t✐✈♦ é ❝❤❛♠❛❞♦ ❞❡ ♣ré✲❛q✉❡❝✐♠❡♥t♦✳
❊ss❡s ❞♦✐s ♠❡❝❛♥✐s♠♦ ❞❡ ❝r✐❛çã♦ ❞❡ ♣❛rtí❝✉❧❛s ♥♦ ✉♥✐✈❡rs♦ ♣r✐♠♦r❞✐❛❧ sã♦ tr❛t❛❞♦s ♣❡❧❛ ❚❡♦r✐❛ ◗✉â♥t✐❝❛ ❞❡ ❈❛♠♣♦s ❡♠ ❡s♣❛ç♦s ❝✉r✈♦s✱ ❡♠ q✉❡ t❡♠♦s ✉♠ ❝❛♠♣♦ ❧✐✈r❡ ❡♠ ✉♠ ❢✉♥❞♦ ❞❡♣❡♥❞❡♥t❡ ❞♦ t❡♠♣♦✱ ♦✉ s❡❥❛✱ ✉♠❛ ♠étr✐❝❛ ❞❡♣❡♥❞❡♥t❡ ❞♦ t❡♠♣♦✳ ❈♦♥t✉❞♦✱ ❛ ❝r✐❛çã♦ ❞❡ ♣❛rtí❝✉❧❛s ♥ã♦ ✜❝❛ ❜❡♠ ❞❡✜♥✐❞❛ ♥❡ss❡ q✉❛❞r♦✱ ✉♠❛ ✈❡③ q✉❡ ❡♠ ❡s♣❛ç♦s✲t❡♠♣♦ ❝✉r✈♦s ♦s ❝♦♥❝❡✐t♦s ❞❡ ✈á❝✉♦ ❡ ♣❛rtí❝✉❧❛s ♥ã♦ ❡stã♦ ❜❡♠ ❞❡✜♥✐❞♦s✳ ❉❡ss❛ ❢♦r♠❛✱ ❝♦♥✈é♠ ♣❡♥s❛r ♥❡ss❡ ♠❡❝❛♥✐s♠♦ ❞❡ ♦✉tr❛ ♠❛♥❡✐r❛✳ ❙❡ t✐✈❡r♠♦s ✉♠ ❝❛♠♣♦ q✉â♥t✐❝♦ ✐♥t❡r❛❣✐♥❞♦ ❝♦♠ ✉♠ ♣♦t❡♥❝✐❛❧ ❡①t❡r♥♦ ❞❡♣❡♥❞❡♥t❡ ❞♦ t❡♠♣♦✱ ♦✉ s❡❥❛✱ ♦ ♣♦t❡♥❝✐❛❧ ❣r❛✈✐t❛❝✐♦♥❛❧ r❡s✲ ♣♦♥sá✈❡❧ ♣❡❧❛ ❡①♣❛♥sã♦ ❞♦ ✉♥✐✈❡rs♦✱ t❡♠♦s q✉❡ ♦ ♠❡❝❛♥✐s♠♦ ❞❡ ❝r✐❛çã♦ ❞❡ ♣❛rtí❝✉❧❛s ♣♦❞❡ s❡r ♠❛✐s ❝❧❛r❛♠❡♥t❡ ❡st✉❞❛❞♦✳ ❱❛♠♦s ♠♦str❛r ♥❡ss❛ ❞✐ss❡rt❛çã♦ q✉❡ ♣♦❞❡♠♦s ❡s❝r❡✈❡r ❞❡
♠❛♥❡✐r❛ t♦t❛❧♠❡♥t❡ ❡q✉✐✈❛❧❡♥t❡ ❛ ❝r✐❛çã♦ ❞❡ ♣❛rtí❝✉❧❛s ❝♦s♠♦❧ó❣✐❝❛ ❝♦♠♦ ✉♠ ♣r♦❜❧❡♠❛ ❞❡ ✉♠ ❝❛♠♣♦ ✐♥t❡r❛❣✐♥❞♦ ❝♦♠ ✉♠ ♣♦t❡♥❝✐❛❧ ❡①t❡r♥♦✳
❊♠ ❡❧❡tr♦❞✐♥â♠✐❝❛ ❡①✐st❡ ✉♠ ❢❡♥ô♠❡♥♦ ❞❡ ❝r✐❛çã♦ ❞❡ ♣❛rtí❝✉❧❛s ♣❡❧❛ ✐♥t❡r❛çã♦ ❞❡ ✉♠ ❝❛♠♣♦ q✉â♥t✐❝♦ ❝♦♠ ✉♠ ❝❛♠♣♦ ❡①t❡r♥♦✿ ♦ ❡❢❡✐t♦ ❙❝❤✇✐♥❣❡r✳ ❖ ♦❜❥❡t✐✈♦ ❞❡ss❛ ❞✐ss❡rt❛çã♦ é ♠♦str❛r q✉❡ ❛ ❝r✐❛çã♦ ❞❡ ♣❛rtí❝✉❧❛s ❝♦s♠♦❧ó❣✐❝❛ ♣♦❞❡ s❡r ❡s❝r✐t❛ ❞❛ ♠❡s♠❛ ❢♦r♠❛ q✉❡ ♦ ❡❢❡✐t♦ ❙❝❤✇✐♥❣❡r✳ ■ss♦ é ✐♠♣♦rt❛♥t❡ ♣♦✐s✱ ❝♦♠♦ ♥ã♦ é ♣♦ssí✈❡❧ t❡st❛r♠♦s ❡ss❡s ♠❡❝❛♥✐s♠♦s ❞❡ ❝r✐❛çã♦ ❝♦s♠♦❧ó❣✐❝♦s✱ ✉♠❛ ✈❡③ q✉❡ ♥ã♦ ♣♦❞❡♠♦s ❝r✐❛r ✉♠ ♥♦✈♦ ✉♥✐✈❡rs♦ q✉❡ ♣❛ss❡ ♣♦r ✉♠❛ ❢❛s❡ ✐♥✢❛❝✐♦♥ár✐❛✱ s❡ ♠♦str❛r♠♦s q✉❡ ❡ss❡s ♠❡❝❛♥✐s♠♦s sã♦ ❛♥á❧♦❣♦s ❛♦s ❞❡ ❝r✐❛çã♦ ❞❡ ♣❛rtí❝✉❧❛s ❞❛ ❡❧❡tr♦❞✐♥â♠✐❝❛✱ ❛ ✈❡r✐✜❝❛çã♦ ❡①♣❡r✐♠❡♥t❛❧ ❡♠ ❚❡rr❛ ❞♦ ❡❢❡✐t♦ ❙❝❤✇✐♥❣❡r s❡r✐❛ ✉♠❛ ❝♦rr♦❜♦r❛çã♦ ❞♦ ♠❡❝❛♥✐s♠♦ ❝♦s♠♦❧ó❣✐❝♦ ❛♥á❧♦❣♦✳
❖ ❡❢❡✐t♦ ❙❝❤✇✐♥❣❡r ❝♦♥s✐st❡ ♥♦ ❢❡♥ô♠❡♥♦ ❞❡ ❝r✐❛çã♦ ❞❡ ♣❛rtí❝✉❧❛s ♣♦r ❝❛♠♣♦s ❡①t❡r♥♦s ❡❧étr✐❝♦s ❡stát✐❝♦s ❡ ♦s❝✐❧❛tór✐♦s✳ ❊ss❡ é ✉♠ ❡❢❡✐t♦ ♥ã♦✲♣❡rt✉r❜❛t✐✈♦ ❡ ♠✉✐t♦ ✐♠♣♦rt❛♥t❡ ❞❛ ❡❧❡tr♦❞✐♥â♠✐❝❛ q✉â♥t✐❝❛ ✭◗❊❉✮ ❡ ♦❝♦rr❡ ❞❡✈✐❞♦ à ✐♥st❛❜✐❧✐❞❛❞❡ ❞♦ ✈á❝✉♦ ❡❧❡tr♦♠❛❣♥ét✐❝♦ q✉❡ ♣♦❞❡ s❡r ♣♦❧❛r✐③❛❞♦ ♣❡❧❛ s✉❛ ✐♥t❡r❛çã♦ ❝♦♠ ✉♠ ❝❛♠♣♦ ❡①t❡r♥♦✳ ❏✉❧✐❛♥ ❙❝❤✇✐♥❣❡r✱ ❡♠ ✶✾✺✶ ❬✼✷❪✱ ❜❛s❡❛❞♦ ♥♦s tr❛❜❛❧❤♦s s❡♠✐♥❛✐s ❞❡ ❢❡♥ô♠❡♥♦s ❞❡ ♣♦❧❛r✐③❛çã♦ ❞♦ ✈á❝✉♦ ❞❡ ❙❛✉t❡r ❬✻✾❪✱ ❊✉❧❡r ❡ ❍❡✐s❡♥❜❡r ❬✼✵❪ ❡ ❲❡✐ss❦♦♣❢ ❬✼✶❪✱ ❢❡③ ♦ ♣r✐♠❡✐r♦ ❝á❧❝✉❧♦ ❞♦ ❡❢❡✐t♦ ❙❝❤✇✐♥❣❡r ❡stát✐❝♦ ✈✐❛ ▲❛❣r❛♥❣❡❛♥❛s ❡❢❡t✐✈❛s ♣❛r❛ ✉♠ ❝❛♠♣♦ ❡❧étr✐❝♦ ❝♦♥st❛♥t❡✱ ❡♠ q✉❡ s❡ ♦❜t❡✈❡ ❛ t❛①❛ ❞❡ ❝r✐❛çã♦ ❞❡ ♣❛rtí❝✉❧❛s ❛ss✐♠ ❝♦♠♦ s❡✉s ❧✐♠✐t❡s ❡①♣❡r✐♠❡♥t❛✐s✳ ❉❡s❞❡ ❡♥tã♦ ❞✐✈❡rs♦s ♠ét♦❞♦s ❢♦r❛♠ ❞❡s❡♥✈♦❧✈✐❞♦s ♣❛r❛ ❞❡s❝r❡✈❡r t❡♦r✐❝❛♠❡♥t❡ ❡ss❡ ❡❢❡✐t♦✱ ❡♠ q✉❡ ♣♦❞❡♠♦s ❞❡st❛❝❛r ♦ ♠ét♦❞♦ ❞❛s tr❛♥s❢♦r♠❛❞❛s ❞❡ ❇♦❣♦❧✐✉❜♦✈✱ ♦ ♠ét♦❞♦ ❞♦ t✉♥❡❧❛♠❡♥t♦ ❬✾✾✱ ✶✵✵❪✱ ♦ ❞❡ ❞❡t❡❝t♦r❡s ❞❡ ♣❛rtí❝✉❧❛s ❬✶✵✶✱ ✶✵✷❪✱ ♦ ♠ét♦❞♦ ❞♦ ❢✉♥❝✐♦♥❛❧ ❞❡ ♦♥❞❛ ❬✶✵✸✱ ✶✵✹❪✱ ❡♥tr❡ ♦✉tr♦s✳ ❖ ❡❢❡✐t♦ ❙❝❤✇✐♥❣❡r ✉t✐❧✐③❛ ❝❛♠♣♦s s♦♠❡♥t❡ ❡❧étr✐❝♦s✱ ✉♠❛ ✈❡③ q✉❡ ❝❛♠♣♦s ♠❛❣♥ét✐❝♦s ♥ã♦ ♣r♦❞✉③❡♠ ♣❛rtí❝✉❧❛s❬✽✼❪✳
❊ss❡ ❡❢❡✐t♦ ❛✐♥❞❛ ♥ã♦ ❢♦✐ ❞❡t❡❝t❛❞♦ ❡①♣❡r✐♠❡♥t❛❧♠❡♥t❡✳ ❙✉❛ ❞❡t❡❝çã♦ é ❞❡ ❣r❛♥❞❡ r❡❧❡✈â♥❝✐❛✱ ✉♠❛ ✈❡③ q✉❡ s❡r✐❛ ❛ ♣r✐♠❡✐r❛ ✈❛❧✐❞❛çã♦ ❞❡ ✉♠ ❡❢❡✐t♦ ♥ã♦✲♣❡rt✉r❜❛t✐✈♦ ❞❛ ◗❊❉ ❬✼✺✱ ✼✻✱ ✼✼❪✱ q✉❡ ❥á é ❢♦rt❡♠❡♥t❡ ❝♦♠♣r♦✈❛❞❛ ♥♦ r❡❣✐♠❡ ♣❡rt✉r❜❛t✐✈♦✳ ❈♦♥t✉❞♦✱ ❛ ❝r✐❛çã♦ ❞❡ ♣❛rtí❝✉❧❛s ♣♦r ❡ss❡ ❡❢❡✐t♦ ❡①✐❣❡ ❝❛♠♣♦s ❡❧étr✐❝♦s ♠✉✐t♦ ❢♦rt❡s ❡ ♥ã♦ r❡❛❧✐③á✈❡✐s ❝♦♠ ❛ t❡❝♥♦❧♦❣✐❛ ❡①♣❡r✐♠❡♥t❛❧ ❛t✉❛❧✳ P♦r ✐ss♦ ❢♦✐ ✐❞❡❛❧✐③❛❞♦✱ ♥♦s ❛♥♦s ✶✾✽✵✱ ♦ ❛♥á❧♦❣♦ ♦s❝✐❧❛tór✐♦ ❞❡ss❡ ❡❢❡✐t♦ ♣❛r❛ ❝❛♠♣♦s ❡①t❡r♥♦s ♦s❝✐❧❛tór✐♦s✱ ❞❛❞♦ q✉❡ ❡ss❡ t✐♣♦ ❞❡ ❝❛♠♣♦ é ♠❛✐s ❢á❝✐❧ ❞❡ s❡r r❡❛❧✐③❛❞♦ ❡①♣❡r✐♠❡♥t❛❧♠❡♥t❡ ❬✼✹❪✳
❖ ❡❢❡✐t♦ ❙❝❤✇✐♥❣❡r ❞✐♥â♠✐❝♦ ❝♦♥s✐st❡ ♥❛ ❝r✐❛çã♦ ❞❡ ♣❛rtí❝✉❧❛s ♣♦r ✉♠ ❝❛♠♣♦ ❡❧étr✐❝♦ ❞❡♣❡♥❞❡♥t❡ ❞♦ t❡♠♣♦✳ ❊ss❡ ❡❢❡✐t♦ ❢♦✐ ❡st✉❞❛❞♦ ♣❛r❛ ❞✐✈❡rs❛s ❢♦r♠❛s ❞♦ ❝❛♠♣♦ ❡①t❡r♥♦ ❛♣❧✐❝❛❞♦✱ s❡♥❞♦ q✉❡ ❛♣r❡s❡♥t❛ s♦❧✉çã♦ ❛♥❛❧ít✐❝❛ ♣❛r❛ ♦ ❝❛s♦ ❞♦ ♣♦t❡♥❝✐❛❧ ❞❡ ❙❛✉t❡r ❬✶✷✸❪✳ ❱❛♠♦s ❡st✉❞❛r ♥❡ss❛ ❞✐ss❡rt❛çã♦ ♦ ❡❢❡✐t♦ ❙❝❤✇✐♥❣❡r ♦s❝✐❧❛tór✐♦✱ ❡♠ q✉❡ ♦ ♣♦t❡♥❝✐❛❧ ❡①✲ t❡r♥♦ é ♦s❝✐❧❛tór✐♦✳ ❊ss❡ ❝❛s♦ é ❞❡ ♠❛✐♦r ✐♥t❡r❡ss❡✱ ✉♠❛ ✈❡③ q✉❡✱ ♣❛r❛ s✉❛ ✈❡r✐✜❝❛çã♦ ❡①♣❡r✐♠❡♥t❛❧✱ ❝❛♠♣♦s ❡❧❡tr♦♠❛❣♥ét✐❝♦s ❞❡ss❛ ❢♦r♠❛ sã♦ ♠❛✐s ❢❛❝✐❧♠❡♥t❡ ♣r♦❞✉③✐❞♦s✱ ❛❧é♠ ❞❡ ♣❡r♠✐t✐r❡♠ ✉♠❛ ❛♥❛❧♦❣✐❛ ❝♦♠ s✐st❡♠❛s ❣r❛✈✐t❛❝✐♦♥❛✐s ❞❡ ❝r✐❛çã♦ ❞❡ ♣❛rtí❝✉❧❛s✳ ❊ss❡ ❡❢❡✐t♦ ❢♦✐ ❡st✉❞❛❞♦ t❡♦r✐❝❛♠❡♥t❡✱ t❛♠❜é♠✱ ♣♦r ❞✐✈❡rs♦s ❢♦r♠❛❧✐s♠♦s✳
❚❡♥t❛t✐✈❛s ❞❡ ❞❡t❡❝çã♦ ❞♦ ❡❢❡✐t♦ ❙❝❤✇✐♥❣❡r ♦s❝✐❧❛tór✐♦ ❛✐♥❞❛ ♥ã♦ ❢♦r❛♠ ❜❡♠ s✉❝❡❞✐❞❛s❀
♦s ❧✐♠✐t❡s ❡①♣❡r✐♠❡♥t❛✐s ♣❛r❛ s✉❛ ❞❡t❡❝çã♦ ❛✐♥❞❛ ♥ã♦ ❢♦r❛♠ ❛❧❝❛♥ç❛❞♦s✳ ❈♦♥t✉❞♦✱ ❡①✐st❡ ✉♠ ❡❢❡✐t♦ q✉â♥t✐❝♦✱ q✉❡ ❝♦♥s✐st❡ ❡♠ ✉♠❛ ❣❡♥❡r❛❧✐③❛çã♦ ❞♦ ❡❢❡✐t♦ ❈❛s✐♠✐r✱ ❡st❡ s✐♠ ♣ró①✐♠♦ ❞❡ s❡r ❞❡t❡❝t❛❞♦✿ ♦ ❡❢❡✐t♦ ❈❛s✐♠✐r ❞✐♥â♠✐❝♦✱ q✉❡ ❝♦♥s✐st❡ ♥❛ ♣r♦❞✉çã♦ ❞❡ ❢ót♦♥s ♣❡❧♦ ♠♦✈✐♠❡♥t♦ ❛❝❡❧❡r❛❞♦ ❞❛✭s✮ ♣❛r❡❞❡✭s✮ ❞❡ ✉♠❛ ❝❛✈✐❞❛❞❡✶ ♥♦ ✈á❝✉♦✳ ❖ ❡①♣❡r✐♠❡♥t♦ ▼■❘✱ ❡♠ ❝♦♥str✉çã♦ ❡ t❡st❡s✱ ❛♣r❡s❡♥t❛✲s❡ ❝♦♠♦ ✉♠❛ ♣♦ssí✈❡❧ ❞❡t❡❝çã♦ ♣❛r❛ ♦ ❡❢❡✐t♦ ❈❛s✐♠✐r ❞✐♥â♠✐❝♦ ❡ ❞❡ ❡❢❡✐t♦s ♥ã♦✲♣❡rt✉r❜❛t✐✈♦s ❞♦ ✈á❝✉♦ q✉â♥t✐❝♦✳ ❘❡s✉❧t❛❞♦s sã♦ ❡s♣❡r❛❞♦s ♣❛r❛ ✷✵✵✾✳
❖ ♣r♦♣ós✐t♦ ❞❡ss❛ ❞✐ss❡rt❛çã♦ é ❢❛③❡r ✉♠❛ ❛♥❛❧♦❣✐❛ ❡♥tr❡ ❛ ❝r✐❛çã♦ ❞❡ ♣❛rtí❝✉❧❛s ♥❛ ✐♥✢❛çã♦ ❡ ♥♦ ♣ré✲❛q✉❡❝✐♠❡♥t♦ ❝♦♠ ♦ ❡❢❡✐t♦ ❙❝❤✇✐♥❣❡r✳ ❆♠❜♦s ♦s ♠❡❝❛♥✐s♠♦s ❝♦♥s✐st❡♠ ❡♠ ♦s❝✐❧❛❞♦r❡s ♣❛r❛♠étr✐❝♦s ❝♦♠ ❢r❡qüê♥❝✐❛ ❞❡♣❡♥❞❡♥t❡ ❞♦ t❡♠♣♦✱ ♠✉❞❛♥❞♦ ❛♣❡♥❛s ❛ ♥❛t✉r❡③❛ ❞♦ ❝❛♠♣♦ ❡①t❡r♥♦ ❛♣❧✐❝❛❞♦✳ Pr♦♣♦♠♦✲♥♦s ❛ ♠♦str❛r q✉❡ ❛ ❝r✐❛çã♦ ❞❡ ♣❛rtí❝✉❧❛s ♥❛ ✐♥✢❛çã♦ ♣♦❞❡ s❡r ❞❡s❝r✐t❛✱ ❛ ♠❡♥♦s ❞❡ ✉♠❛ tr❛♥s❢♦r♠❛çã♦ ❝❛♥ô♥✐❝❛✱ ♣❡❧❛s ♠❡s♠❛s ❡q✉❛çõ❡s q✉❡ ❞❡s❝r❡✈❡♠ ❛ ❝r✐❛çã♦ ❞❡ ♣❛rtí❝✉❧❛s ♣❛r❛ ♦ ❡❢❡✐t♦ ❙❝❤✇✐♥❣❡r ❡stát✐❝♦✱ s❡♥❞♦ ❛ss✐♠ ❡q✉✐✈❛❧❡♥t❡s✳ ◆♦ ❝❛s♦ ❞♦ ♣ré✲❛q✉❡❝✐♠❡♥t♦✱ ♠♦str❛r❡♠♦s q✉❡ ❛ ❝r✐❛çã♦ ❞❡ ♣❛rtí✲ ❝✉❧❛s ♣♦❞❡ s❡r ❞❡s❝r✐t❛ ♣♦r ✉♠❛ ❡q✉❛çã♦ ❞❡ ▼❛t❤✐❡✉✱ ❛ss✐♠ ❝♦♠♦ ♥♦ ❡❢❡✐t♦ ❙❝❤✇✐♥❣❡r ♦s❝✐❧❛tór✐♦✳ ❆ss✐♠✱ ❝♦♠ ❛ ♠❡❞✐çã♦ ❞♦ ❡❢❡✐t♦ ❙❝❤✇✐♥❣❡r ♣♦❞❡♠♦s ❝♦♥✜r♠❛r q✉❡ ❡ss❡ ❡❢❡✐t♦ ♥ã♦✲♣❡rt✉r❜❛t✐✈♦ ❞❡ ❝r✐❛çã♦ ❞❡ ♣❛rtí❝✉❧❛s ❞♦ ✈á❝✉♦ é r❡❛❧✐③á✈❡❧ ❡ ❝♦♠ ✐ss♦ ♣♦ssí✈❡❧ ❞❡ t❡r ❛❝♦♥t❡❝✐❞♦ ♥♦ ✉♥✐✈❡rs♦ ♣r✐♠♦r❞✐❛❧✳
❈♦♠♦ ♦ t❡♠❛ ❝❡♥tr❛❧ ❞❡ ✐♥✈❡st✐❣❛çã♦ ♥❛ ❞✐ss❡rt❛çã♦ é ❛ ❝♦♠♣❛r❛çã♦ ❡♥tr❡ ♦s ❡❢❡✐✲ t♦s ❙❝❤✇✐♥❣❡r ❡stát✐❝♦ ❡ ♦s❝✐❧❛tór✐♦ ❝♦♠ ❛ ❝r✐❛çã♦ ❞❡ ♣❛rtí❝✉❧❛s ♥❛ ✐♥✢❛çã♦ ❡ ♥♦ ♣ré✲ ❛q✉❡❝✐♠❡♥t♦✱ ❞❡♠♦str❛♥❞♦ q✉❡ ❡ss❡s ❞♦✐s ❢❡♥ô♠❡♥♦s sã♦ ❞❡s❝r✐t♦s ❜❛s✐❝❛♠❡♥t❡ ♣❡❧❛ ♠❡s♠❛ t❡♦r✐❛✱ ❡ss❛ ✈❡r✐✜❝❛çã♦ ❝❡♥tr❛❧ s❡rá ❢❡✐t❛ ♥♦ ❝♦♥t❡①t♦ ❞♦ ❢♦r♠❛❧✐s♠♦ ❞❛s tr❛♥s❢♦r♠❛❞❛s ❞❡ ❇♦❣♦❧✐✉❜♦✈✳ ◆❛ ❞✐ss❡rt❛çã♦ ❞❡s❝r❡✈❡♠♦s ❞❡t❛❧❤❛❞❛♠❡♥t❡ ♦ ❢♦r♠❛❧✐s♠♦ ❣❡r❛❧ ❞♦ ❡❢❡✐t♦ ❙❝❤✇✐♥❣❡r ❡stát✐❝♦✱ q✉❡ ♥♦s ♣❡r♠✐t✐rá ❛ ❝♦♠♣❛r❛çã♦ ❝♦♠ ♦ ❢♦r♠❛❧✐s♠♦ q✉❡ ❞❡s❝r❡✈❡ ❛ t❡♦r✐❛ ❞❛ ✐♥✢❛çã♦✳ ❆ ❝r✐❛çã♦ ❞❡ ♣❛rtí❝✉❧❛s é ❞❡s❝r✐t❛ ✈✐❛ três ❢♦r♠❛❧✐s♠♦s✿ ♦ ❞❛ t❡♦r✐❛ ❞♦ ❡s♣❛❧❤❛♠❡♥t♦✱ ✈✐❛ ❛ t❡♦r✐❛ ❞❡ tr❛♥s❢♦r♠❛❞❛s ❞❡ ❇♦❣♦❧✐✉❜♦✈ ❡ ✈✐❛ ❡st❛❞♦s sq✉❡❡③❡❞✳ ❆ ❞❡s❝r✐çã♦ ✈✐❛ t❡♦r✐❛ ❞❡ ❡s♣❛❧❤❛♠❡♥t♦✱ ❛♣❡s❛r ❞❡ s❡r ❛♣r❡s❡♥t❛❞❛ ❞❡ ❢♦r♠❛ ❞❡t❛❧❤❛❞❛✱ s❡r✈❡✲♥♦s s✐♠♣❧❡s♠❡♥t❡ ♣❛r❛ ❛ ♦❜t❡♥çã♦ ❞♦s ❧✐♠✐t❡s ❡①♣❡r✐♠❡♥t❛✐s ❞❡ ♦❜s❡r✈❛çã♦ ❞♦ ❡❢❡✐t♦✳ ❖ t❡♠❛ ❝❡♥tr❛❧ ❞♦ ❝❛♣ít✉❧♦ ❞♦ ❡❢❡✐t♦ ❙❝❤✇✐♥❣❡r ❡stát✐❝♦ é✱ ♣♦rt❛♥t♦✱ ♦ ❢♦r♠❛❧✐s♠♦ ✈✐❛ tr❛♥s❢♦r♠❛❞❛s ❞❡ ❇♦❣♦❧✐✉❜♦✈ ❡ ✈✐❛ ❡st❛❞♦s sq✉❡❡③❡❞✳
P❛r❛ ♦ ❡❢❡✐t♦ ❙❝❤✇✐♥❣❡r ♦s❝✐❧❛tór✐♦✱ ❞❡ ♠❛♥❡✐r❛ ❛♥á❧♦❣❛ ❛♦ ❝❛s♦ ❡stát✐❝♦✱ t❡♠♦s ♦ ❡❢❡✐t♦ ❞❡s❝r✐t♦ ✈✐❛ três ❢♦r♠❛❧✐s♠♦s✳ ◆♦✈❛♠❡♥t❡✱ ❛♣❡s❛r ❞❡ s✉❛ ❞❡s❝r✐çã♦ ❡①t❡♥s❛ ❡ ❞❡t❛❧❤❛❞❛✱ ♦ ❝á❧❝✉❧♦ ✈✐❛ t❡♦r✐❛ ❞❡ ❡s♣❛❧❤❛♠❡♥t♦ ❢❛rá ❝♦♠ q✉❡ ♦❜t❡♥❤❛♠♦s ♦s ❧✐♠✐t❡s ♦❜s❡r✈❛❝✐♦♥❛✐s ❞❡ss❡ ❡❢❡✐t♦✳ ❊❧❡s s❡rã♦ ❝♦♥s✐❞❡r❛❞♦s ♥❛ ❛♥á❧✐s❡ ❞♦ ❝❛s♦ ❝❡♥tr❛❧ ❞❡ ✐♥t❡r❡ss❡✱ q✉❡ é ❛ ❞❡s❝r✐çã♦ ✈✐❛ tr❛♥s❢♦r♠❛❞❛s ❞❡ ❇♦❣♦❧✐✉❜♦✈✳ ◆♦ ❝❛s♦ ♦s❝✐❧❛tór✐♦✱ ♦ ❢♦r♠❛❧✐s♠♦ ✉t✐❧✐③❛❞♦ ♣❛r❛ ❝♦♠♣✉t❛r ❡ss❡ ❡❢❡✐t♦ ❢♦✐ ❛♣❧✐❝❛❞♦ ❛q✉✐ ♣❡❧❛ ♣r✐♠❡✐r❛ ✈❡③ ♣❛r❛ ❡ss❡ t✐♣♦ ❞❡ s✐st❡♠❛✱ ❡
✶◆ã♦ ♥❡❝❡ss❛r✐❛♠❡♥t❡ ✉♠❛ ❝❛✈✐❞❛❞❡✳ ❊ss❡ ❡❢❡✐t♦ ♦❝♦rr❡ t❛♠❜é♠ ❡♠ ♣❧❛❝❛s ♣❛r❛❧❡❧❛s ♥♦ ✈á❝✉♦✱ ❡♠
✉♠❛ ú♥✐❝❛ ♣❧❛❝❛ ♥♦ ✈á❝✉♦✱ ❡♥tr❡ ♦✉tr❛s ❝♦♥✜❣✉r❛çõ❡s✳
❜❛s❡✐❛✲s❡ ♥❛ ❛♥á❧✐s❡ ❢❡✐t❛ ♣❛r❛ ❛ ❝r✐❛çã♦ ❞❡ ♣❛rtí❝✉❧❛s ♣♦r r❡ss♦♥â♥❝✐❛ ♣❛r❛♠étr✐❝❛ ♥♦ ♣ré✲ ❛q✉❡❝✐♠❡♥t♦✳ ◆♦ ❝❛♣ít✉❧♦ ❞♦ ❡❢❡✐t♦ ♦s❝✐❧❛tór✐♦ ❛♣r❡s❡♥t❛♠♦s✱ t❛♠❜é♠✱ ♦ ❡❢❡✐t♦ ❈❛s✐♠✐r ❞✐♥â♠✐❝♦✱ ❛♥á❧♦❣♦ ❞✐♥â♠✐❝♦ ❞♦ ❝♦♥❤❡❝✐❞♦ ❡❢❡✐t♦ ❈❛s✐♠✐r✱ ♥♦ q✉❛❧ ❛ ♦s❝✐❧❛çã♦ ❞❛ ♣❧❛❝❛s ❞♦ ❝❛♣❛❝✐t♦r q✉❡ ❡stã♦ ❝♦❧♦❝❛❞♦ ♥♦ ✈á❝✉♦ ❢❛③ ♦ ♣❛♣❡❧ ❞♦ ❝❛♠♣♦ ❡①t❡r♥♦ ❛♣❧✐❝❛❞♦ ❬✶✸✻✱ ✼✾✱ ✽✵❪✳ ❊ss❡ ❡❢❡✐t♦ é ❛♣r❡s❡♥t❛❞♦ ♣♦r s❡r ✉♠ ❡❢❡✐t♦ ❛♥á❧♦❣♦ ❛♦ ❙❝❤✇✐♥❣❡r ♦s❝✐❧❛tór✐♦✱ ♠❛s ♣r✐♥❝✐♣❛❧♠❡♥t❡ ♣♦rq✉❡✱ ♣❡❧❛ ❛✉sê♥❝✐❛ ❞❡ ❡①♣❡r✐♠❡♥t♦s ❞❡ ❞❡t❡❝çã♦ ♣ró①✐♠❛ ❞♦ ❡❢❡✐t♦ ❙❝❤✇✐♥❣❡r✱ é ❡❧❡ q✉❡ ❡stá ♠❛✐s ♣ró①✐♠♦ ❞❡ s❡r ❞❡t❡❝t❛❞♦✳ ◆♦✈❛♠❡♥t❡✱ ❛ ❞❡s❝r✐çã♦ ❞❡ss❡ ❡❢❡✐t♦ é ❞❡t❛❧❤❛❞❛ ❡ ❡①t❡♥s❛✱ ♠❛s ♦ ✐♠♣♦rt❛♥t❡ ❛ s❡r ❧❡✈❛❞♦ ❡♠ ❝♦♥t❛ é ❛ ✈❡r✐✜❝❛çã♦ ❞❡ q✉❡ ♣♦❞❡ s❡r ❡♥t❡♥❞✐❞♦ ❝♦♠♦ ✉♠ ❡❢❡✐t♦ ❛♥á❧♦❣♦ ❛♦ ❙❝❤✇✐♥❣❡r ♦s❝✐❧❛tór✐♦ ❡ ❧❡✈❛✲♥♦s✱ ❛♦ ✜♥❛❧✱ ❛ ✉♠ ♥ú♠❡r♦ ❞❡ ♣❛rtí❝✉❧❛s ❝r✐❛❞❛s q✉❡ ♣♦ss✐❜✐❧✐t❛ ❛ ❞❡t❡❝çã♦ ❡①♣❡r✐♠❡♥t❛❧✳
❖r❣❛♥✐③❛♠♦s ❛ ❞✐ss❡rt❛çã♦ ❞❛ s❡❣✉✐♥t❡ ♠❛♥❡✐r❛✳ ◆♦ ❝❛♣ít✉❧♦ ✷ ❞❛r❡♠♦s ✉♠❛ ✐♥tr♦✲ ❞✉çã♦ ❞♦ ♠♦❞❡❧♦ ❝♦s♠♦❧ó❣✐❝♦ ♣❛❞rã♦✱ ✐❞❡♥t✐✜❝❛♥❞♦ ♦s ❛s♣❡❝t♦s ❞❛ ❡str✉t✉r❛✱ ❡①♣❛♥sã♦ ❡ ❡✈♦❧✉çã♦ ❞♦ ✉♥✐✈❡rs♦✳ ■❞❡♥t✐✜❝❛r❡♠♦s t❛♠❜é♠ ♦s ♣r♦❜❧❡♠❛s q✉❡ ❧✐♠✐t❛♠ ❡ss❡ ♠♦❞❡❧♦✳ ❈♦♠ ✐ss♦✱ ♣❛rt✐r❡♠♦s ♣❛r❛ ♦ ❈❛♣ít✉❧♦ ✸✱ ❡♠ q✉❡ ❞❡s❡♥✈♦❧✈❡♠♦s ❛ t❡♦r✐❛ ❞❛ ✐♥✢❛çã♦ ❡ ❞♦ ♣ré✲❛q✉❡❝✐♠❡♥t♦ ❡ r❡❛q✉❡❝✐♠❡♥t♦✳ ▼♦str❛r❡♠♦s ❝♦♠♦ ❡ss❛ t❡♦r✐❛ r❡s♦❧✈❡ ♦s ♣r♦❜❧❡♠❛s ❞♦ ♠♦❞❡❧♦ ❞♦ ❇✐❣ ❇❛♥❣✱ s✉❛ t❡♦r✐❛ ❣❡r❛❧ ❡ s❡✉ ♣❡rí♦❞♦ ✜♥❛❧ ❡♠ q✉❡ q✉❛s❡ t♦❞❛s ❛s ♣❛rtí✲ ❝✉❧❛s ❡❧❡♠❡♥t❛r❡s ❞♦ ✉♥✐✈❡rs♦ ❢♦r❛♠ ❝r✐❛❞❛s✱ ♦ r❡❛q✉❡❝✐♠❡♥t♦✳ ❊♠ s❡❣✉✐❞❛✱ ♥❛ ❈❛♣ít✉❧♦ ✹✱ ❞❡s❝r❡✈❡r❡♠♦s ❛ t❡♦r✐❛ ❞❛s ♣❡rt✉r❜❛çõ❡s ❝♦s♠♦❧ó❣✐❝❛s✱ ❛♥❛❧✐s❛♥❞♦ t❛♥t♦ s✉❛ ❡✈♦❧✉çã♦ ❝♦♠♦ s❡✉ s✉r❣✐♠❡♥t♦ ❞❡✈✐❞♦ às ✢✉t✉❛çõ❡s q✉â♥t✐❝❛s ♥❛ ✐♥✢❛çã♦✳ P❛rt✐r❡♠♦s ❡♥tã♦ ♣❛r❛ ❛ ❞❡s❝r✐çã♦ ❞♦ ❡❢❡✐t♦ ❙❝❤✇✐♥❣❡r ❡stát✐❝♦✱ ♥♦ ❈❛♣ít✉❧♦ ✺ ❡ ♦s❝✐❧❛tór✐♦ ♥♦ ❈❛♣ít✉❧♦ ✻✳ ◆♦ ❈❛♣ít✉❧♦ ✺✱ ❞❛r❡♠♦s ✉♠❛ ✐♥tr♦❞✉çã♦ t❡♦r✐❛ q✉â♥t✐❝❛ ❞❡ ❝❛♠♣♦s ♥❛ ♣r❡s❡♥ç❛ ❞❡ ❝❛♠♣♦s ❡①t❡r♥♦s ❡ ❞❡s❝r❡✈❡r❡♠♦s ♦ ❡❢❡✐t♦ ❙❝❤✇✐♥❣❡r ❡♠ três ❞✐❢❡r❡♥t❡s ❢♦r♠❛❧✐s♠♦s✳ ◆♦ ❈❛♣ít✉❧♦ ✻✱ ❞❡s❝r❡✈❡r❡♠♦s ❛ ❝r✐❛çã♦ ❞❡ ♣❛rtí❝✉❧❛s ♣♦r ✉♠ ❝❛♠♣♦ ❡①t❡r♥♦ ♦s❝✐❧❛tór✐♦✱ ❞❡t❡r♠✐♥❛♥❞♦ t❛♠❜é♠ s❡✉s ❧✐♠✐t❡s ♦❜s❡r✈❛❝✐♦♥❛✐s✳ ❈♦♠ ✐ss♦✱ ✐♥tr♦❞✉③✐r❡♠♦s ♦ ❡❢❡✐t♦ ❈❛s✐♠✐r ❞✐♥â♠✐❝♦✱ q✉❡ r❡♣r❡s❡♥t❛ ❛ ♠❛✐s ♣r♦♠✐ss♦r❛ ❝❤❛♥❝❡ ❞❡ ♦❜s❡r✈❛çã♦ ❞❛ ❝r✐❛çã♦ ❞❡ ♣❛rtí❝✉❧❛s ❞♦ ✈á❝✉♦ ♣♦r ✉♠ ❝❛♠♣♦ ❡①t❡r♥♦✳ ❊♠ s❡❣✉✐❞❛✱ ♥♦ ❈❛♣ít✉❧♦ ✼✱ s❡rá ❞❡s❝r✐t♦ ♦ t❡♠❛ ❝❡♥tr❛❧ ❞❡ss❛ ❞✐ss❡rt❛çã♦✱ q✉❛♥❞♦ ❢❛r❡♠♦s ❛ ❛♥❛❧♦❣✐❛ ❡♥tr❡ ♦s s✐st❡♠❛s ❝♦s♠♦❧ó❣✐❝♦s ❡ ❡❧❡tr♦♠❛❣♥ét✐❝♦s✱ ♠♦str❛♥❞♦✱ ♥♦ ✜♠✱ q✉❡ sã♦ ❡q✉✐✈❛❧❡♥t❡s✳ ❈♦♥❝❧✉í♠♦s ♦ tr❛❜❛❧❤♦✱ ❡♥tã♦✱ ♥♦ ❈❛♣ít✉❧♦ ✽✳
❈❛♣ít✉❧♦ ✷
▼♦❞❡❧♦ ❈♦s♠♦❧ó❣✐❝♦ P❛❞rã♦
❖ ▼♦❞❡❧♦ ❈♦s♠♦❧ó❣✐❝♦ P❛❞rã♦ ✭▼❈P✮ ✭♦✉ ❚❡♦r✐❛ ❞♦ ❇✐❣ ❇❛♥❣ ◗✉❡♥t❡✮ é ❛ ❜❛s❡ ♣❛r❛ ♦ ♥♦ss♦ ❛t✉❛❧ ❡♥t❡♥❞✐♠❡♥t♦ ❡ r❡♣r❡s❡♥t❛çã♦ ❞♦ ✉♥✐✈❡rs♦✱ ❞❡s❝r❡✈❡♥❞♦ s✉❛ ❡✈♦❧✉çã♦ ❛ ♣❛rt✐r ❞❡ ✉♠ ❡st❛❞♦ ✐♥❝✐❛❧ ❞❡ ❣r❛♥❞❡ ❞❡♥s✐❞❛❞❡ ❡ t❡♠♣❡r❛t✉r❛ ❤á ❛♣r♦①✐♠❛❞❛♠❡♥t❡ ✶✸✱✾ ❜✐❧❤õ❡s ❞❡ ❛♥♦s ❡ q✉❡ ✈❡♠ s❡ ❡①♣❛♥❞✐♥❞♦ ❡ ❡s❢r✐❛♥❞♦ ❞❡s❞❡ ❡♥tã♦✳ ◆❡ss❡ ♠♦❞❡❧♦ t❡♠♦s ✉♠ ✉♥✐✈❡rs♦ ❤♦♠♦❣ê♥❡♦ ❡ ✐s♦tró♣✐❝♦✱ ❛♣r♦①✐♠❛❞❛♠❡♥t❡ ♣❧❛♥♦✱ ❝♦♠♣♦st♦ ♣r✐♥❝✐♣❛♠❡♥t❡ ♣♦r ♠❛tér✐❛ ❜❛r✐ô♥✐❝❛ ✭∼ 4%✮✱ r❛❞✐❛çã♦ ❡❧❡tr♦♠❛❣♥ét✐❝❛ ✭∼ 0,001%✮✱ ✉♠ t✐♣♦ ❞❡ ♠❛tér✐❛ q✉❡ ♥ã♦
s❛❜❡♠♦s ❛ ♦r✐❣❡♠✱ ❞❡♥♦♠✐♥❛❞❛ ♠❛tér✐❛ ❡s❝✉r❛ ✭∼23%✮ ❡ ✉♠❛ ❡♥❡r❣✐❛ t❛♠❜é♠ ❞❡ ♦r✐❣❡♠
❞❡s❝♦♥❤❡❝✐❞❛✱ ❝❤❛♠❛❞❛ ❡♥❡r❣✐❛ ❡s❝✉r❛ ✭∼73%✮❬✷✷✱ ✷✸✱ ✷✹✱ ✷✺❪✳ ❊ss❡ ♠♦❞❡❧♦ é ❛♠♣❧❛♠❡♥t❡
❛❝❡✐t♦ ❡ ❝♦❧❡❝✐♦♥❛ ✉♠❛ ❣r❛♥❞❡ q✉❛♥t✐❞❛❞❡ ❞❡ s✉❝❡ss♦s t❡ór✐❝♦s ❡ ♦❜s❡r✈❛❝✐♦♥❛✐s✳ ❆♣❡s❛r ❞❡ ❛♣r❡s❡♥t❛r ❛❧❣✉♥s ♣r♦❜❧❡♠❛s ❡ ♥❡❝❡ss✐t❛r ❞❡ t❡♦r✐❛s ❝♦♠♣❧❡♠❡♥t❛r❡s✱ ❛✐♥❞❛ é ♦ ♠♦❞❡❧♦ ❛❞♦t❛❞♦ ♣❛r❛ ❞❡s❝r❡✈❡r ❛ ❡str✉t✉r❛✱ ❡①♣❛♥sã♦ ❡ ❡✈♦❧✉çã♦ ❞♦ ✉♥✐✈❡rs♦✳
❖ ▼❈P ❜❛s❡✐❛✲s❡ ❡♠ ❞♦✐s ♣✐❧❛r❡s t❡ór✐❝♦s✿ ❛ t❡♦r✐❛ ❞❛ r❡❧❛t✐✈✐❞❛❞❡ ❣❡r❛❧✱ q✉❡ s✉♣♦♠♦s ❞❡s❝r❡✈❡r ❛ ❞✐♥â♠✐❝❛ ❞♦ ✉♥✐✈❡rs♦ ❝♦♠♦ ✉♠ t♦❞♦✱ ❡ ♦ ♣r✐♥❝í♣✐♦ ❝♦s♠♦❧ó❣✐❝♦✱ ❤✐♣ót❡s❡ s✐♠✲ ♣❧✐✜❝❛❞♦r❛ q✉❡ ❛✜r♠❛ q✉❡ ♦ ✉♥✐✈❡rs♦ é ❡s♣❛❝✐❛❧♠❡♥t❡ ❤♦♠♦❣ê♥❡♦ ❡ ✐s♦tró♣✐❝♦✳ ❆❧é♠ ❞✐ss♦✱ ❡❧❡ s❡ ❛♣♦✐❛ ❡♠ três ♣✐❧❛r❡s ♦❜s❡r✈❛❝✐♦♥❛✐s✿ ❛ ❧❡✐ ❞❡ ❍✉❜❜❧❡✱ q✉❡ ♠♦str❛ q✉❡ ♦ ✉♥✐✈❡rs♦ ❡stá ❡♠ ❡①♣❛♥sã♦❀ ❛ ❛❜✉♥❞â♥❝✐❛ ❞♦s ❡❧❡♠❡♥t♦s ❧❡✈❡s✱ q✉❡ ❝♦♥✜r♠❛ ❛s ❤✐♣ót❡s❡s ❞❛ ♥✉❝❧❡✲ ♦ssí♥t❡s❡ ♣r✐♠♦r❞✐❛❧❀ ❡ ❛ r❛❞✐❛çã♦ ❝ós♠✐❝❛ ❞❡ ❢✉♥❞♦ ✭❘❈❋✮✱ ✉♠❛ r❛❞✐❛çã♦ ✐s♦tró♣✐❝❛✱ ❞❡ ❝♦r♣♦ ♥❡❣r♦✱ ❝♦♠ t❡♠♣❡r❛t✉r❛ ❞❡ ❛♣r♦①✐♠❛❞❛♠❡♥t❡ ✷✱✼✺❑✳
❖ ▼❈P ❞❡s❝r❡✈❡ ❝♦♠ ❜♦❛ ♣r❡❝✐sã♦ ♦s ❛s♣❡❝t♦s ❣❡♦♠étr✐❝♦s ❞♦ ✉♥✐✈❡rs♦✱ ❞❡✜♥✐♥❞♦ s✉❛ ❡str✉t✉r❛ ❡ s✉❛ ❡✈♦❧✉çã♦ ❞✐♥â♠✐❝❛✱ ♠❛s t❛♠❜é♠ ♣r❡✈ê ❞❡ ♠❛♥❡✐r❛ ♠✉✐t♦ ♣r❡❝✐s❛ ❛ ❛❜✉♥❞â♥❝✐❛ ❞❡ s❡✉s ❝♦♠♣♦♥❡♥t❡s ♠❛t❡r✐❛✐s✳ ▼♦str❛r❡♠♦s ♥❡ss❡ ❝❛♣ít✉❧♦ ♣r✐♠❡✐r❛♠❡♥t❡ ❛s ♣r❡✈✐sõ❡s ❣❡♦♠étr✐❝❛s ❞♦ ♠♦❞❡❧♦✱ ❡①♣♦♥❞♦ ♦s ❝♦♥❝❡✐t♦s ❡ ❡q✉❛çõ❡s ❜ás✐❝❛s q✉❡ ❡♠❡r❣❡♠ ❞❡ss❛ t❡♦r✐❛ ❡ ✐♥tr♦❞✉③✐♥❞♦ s❡✉s ♣❛râ♠❡tr♦s ❝♦s♠♦❧ó❣✐❝♦s ❞❡ r❡❧❡✈â♥❝✐❛ ❡ s✉❛s r❡❧❛çõ❡s✳ P♦❞❡♠♦s ❛ss✐♠ ❞❡s❝r❡✈❡r ♦ ▼❈P ❞❡ ♠❛♥❡✐r❛ ❣❡r❛❧✱ ❛♣r❡s❡♥t❛♥❞♦ t❛♠❜é♠ s✉❛s ♣r❡✈✐sõ❡s s♦❜r❡ ❛ ❛❜✉♥❞â♥❝✐❛ ❞♦s ❡❧❡♠❡♥t♦s q✉í♠✐❝♦s ❡ ❞❡s❝r❡✈❡♥❞♦ ❛ ❤✐stór✐❛ tér♠✐❝❛ ❞♦ ✉♥✐✈❡rs♦✳ ❆♣ós ❞❡✜♥✐r♠♦s ♦ ♠♦❞❡❧♦✱ ❛♣r❡s❡♥t❛r❡♠♦s s❡✉s ♣✐❧❛r❡s ♦❜s❡r✈❛❝✐♦♥❛✐s ❡ ♣r✐♥❝✐♣❛✐s ♣r♦❜❧❡✲ ♠❛s ❞❛ t❡♦r✐❛✳
