Geometreia de Weyl

❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❛ P❛r❛í❜❛
❈❡♥tr♦ ❞❡ ❈✐ê♥❝✐❛s ❊①❛t❛s ❡ ❞❛ ◆❛t✉r❡③❛
❉❡♣❛rt❛♠❡♥t♦ ❞❡ ❋ís✐❝❛
❚❡s❡ ❞❡ ❉♦✉t♦r❛❞♦

❚❡♦r✐❛ ❡s❝❛❧❛r✲t❡♥s♦r✐❛❧✿
❯♠❛ ❛❜♦r❞❛❣❡♠ ❣❡♦♠étr✐❝❛
❚♦♥② ❙✐❧✈❛ ❆❧♠❡✐❞❛

❏♦ã♦ P❡ss♦❛✱ ❏✉❧❤♦ ❞❡ ✷✵✶✹

❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❛ P❛r❛í❜❛
❈❡♥tr♦ ❞❡ ❈✐ê♥❝✐❛s ❊①❛t❛s ❡ ❞❛ ◆❛t✉r❡③❛
❉❡♣❛rt❛♠❡♥t♦ ❞❡ ❋ís✐❝❛
❚❡s❡ ❞❡ ❉♦✉t♦r❛❞♦

❚❡♦r✐❛ ❡s❝❛❧❛r✲t❡♥s♦r✐❛❧✿
❯♠❛ ❛❜♦r❞❛❣❡♠ ❣❡♦♠étr✐❝❛
❚♦♥② ❙✐❧✈❛ ❆❧♠❡✐❞❛
❚❡s❡ s✉❜♠❡t✐❞❛ ❛♦ ❉❡♣❛rt❛♠❡♥t♦ ❞❡
❋ís✐❝❛

❞❛

❯♥✐✈❡rs✐❞❛❞❡

❋❡❞❡r❛❧

❞❛

P❛r❛í❜❛✱ s♦❜ ♦r✐❡♥t❛çã♦ ❞♦ ♣r♦❢❡ss♦r
❉r✳

❈❛r❧♦s ❆✉❣✉st♦ ❘♦♠❡r♦ ❋✐❧❤♦✱

❝♦♠♦ ♣❛rt❡ ❞♦s r❡q✉✐s✐t♦s ♣❛r❛ ♦❜✲ t❡♥çã♦ ❞♦ tít✉❧♦ ❞❡ ❉♦✉t♦r ❡♠ ❋í✲ s✐❝❛✳ ❏♦ã♦ P❡ss♦❛✱ ❢❡✈❡r❡✐r♦ ❞❡ ✷✵✶✹

❩❛❩❡◆

❙✉♠ár✐♦
❘❡s✉♠♦

✐✐✐

❆❜str❛❝t

✐✈

■♥tr♦❞✉çã♦

✶

✶

✸

❊s♣❛ç♦✲t❡♠♣♦ ❞❡ ❲❡②❧ ✐♥t❡❣rá✈❡❧ ✭❲■❙❚✮

✶✳✶
✶✳✷
✶✳✸

●❡♥❡r❛❧✐③❛çã♦ ❞❛ ❣❡♦♠❡tr✐❛ r✐❡♠❛♥♥✐❛♥❛ ✳ ✳ ✳
❈✉r✈❛t✉r❛ ❞❡ ❲❡②❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳
✶✳✷✳✶ ❈✉r✈❛t✉r❛ ❞❡ ❲❡②❧ ♥ã♦✲✐♥t❡❣rá✈❡❧ ✳ ✳ ✳
✶✳✷✳✷ ■❞❡♥t✐❞❛❞❡ ❞❡ ❇✐❛♥❝❤✐✲ ❲❡②❧ ✐♥t❡❣rá✈❡❧
■♥✈❛r✐â♥❝✐❛ ❞❛ ❛çã♦ ❡ ❣❡♦♠❡tr✐❛ ❞❡ ❲❡②❧ ✳ ✳ ✳

✳
✳
✳
✳
✳

✳
✳
✳
✳
✳

❚❡♦r✐❛ ❞❡ ❇r❛♥s✲❉✐❝❦❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳
▲✐♠✐t❡ ❞❡ ❇❉ ♣❛r❛ ❘● ❖✭ ω1 ✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳
✷✳✷✳✶ ▲✐♠✐t❡ ❞❡ ❇❉ t♦ ❘● ❖✭ √1ω ✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳
❚r❛♥s❢♦r♠❛çõ❡s ❝♦♥❢♦r♠❡s ❡ r❡❢❡r❡♥❝✐❛❧ ❞❡ ❊✐♥st❡✐♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳
✷✳✸✳✶ ❘❡❢❡r❡♥❝✐❛❧ ❞❡ ❊✐♥st❡✐♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳
❙♦❧✉çõ❡s ❡stát✐❝❛s ❝♦♠ s✐♠❡tr✐❛ ❡s❢ér✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳
✷✳✹✳✶ ❙♦❧✉çã♦ ❞❡ ❈❛♠♣❛♥❡❧❧✐✲▲♦✉st♦ ♥♦ r❡❢❡r❡♥❝✐❛❧ ❞❡ ❊✐♥st❡✐♥ ✳ ✳ ✳ ✳ ✳
❙✐♠✐❧❛r✐❞❛❞❡s ❡♥tr❡ ❛ t❡♦r✐❛ ❞❡ ❇❉ ❡ ❣❡♦♠❡tr✐❛ ❞❡ ❲❡②❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳
✷✳✺✳✶ ❆ tr❛♥s❢♦r♠❛çã♦ ❞❡ ❲❡②❧ ❝♦♠♦ tr❛♥s❢♦r♠❛çã♦ ❞❡ ✉♥✐❞❛❞❡s ✳ ✳ ✳ ✳
✷✳✺✳✷ ❈♦♥s❡r✈❛çã♦ ❞❡ ❡♥❡r❣✐❛✲♠♦♠❡♥t♦ ♠♦❞✐✜❝❛❞❛ ❡ ❣❡♦❞és✐❝❛s ❞❡ ❲❡②❧

✳
✳
✳
✳
✳
✳
✳
✳
✳
✳

✷ ❚❡♦r✐❛s ❡s❝❛❧❛r❡s✲t❡♥s♦r✐❛✐s
✷✳✶
✷✳✷

✷✳✸
✷✳✹
✷✳✺

✸ ❚❡♦r✐❛ ❡s❝❛❧❛r✲t❡♥s♦r✐❛❧ ❣❡♦♠étr✐❝❛