УК гд а Уж × в
УК гд а Уж × в
УК гд а Уж × в
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ØÔÖÓÙÖØÓÖÓÒÞØÐÖ¸ÚÒØÒÓÑÒØÓÖÒØØݸØÛÐÐÙ<strong>×</strong>ÙÐØÓ ÔØÖºÃÅÄ<strong>×</strong>ÙÔÖÐÖ<strong>×</strong>ÖÓÑÝÓÒËÔØÖ<br />
Ð<strong>×</strong>Ø<strong>×</strong>ÓÑÓØÓ<strong>×</strong>ÖÚØÓÒ<strong>×</strong>ØØÒÑÓÙØØÜÔÒ<strong>×</strong>ÓÒ<strong>×</strong>ÓØÑÓÙÐÖÓÖÑ<br />
º¿º ÒÐÝÞÒØÅÓÙÐÖÓÖÑ<strong>×</strong> )ÒØÖÒÒÖÔÖÓÙØÛØ ½ºÍ<strong>×</strong>ÒØÜÔÖ<strong>×</strong><strong>×</strong>ÓÒ<strong>×</strong>ÓÖØÖÐ<strong>×</strong>ÑÔÐÖÓÓØ<strong>×</strong>¸(δ 1 , δ 2 , δ 3<br />
Z¸ÓÒ<strong>×</strong><strong>×</strong>ØØe 1/2ºÙÖØÖ¸ÓÒ<strong>×</strong>ØÒØØÓÒÖÐØÒØÖÓÓØ<br />
−πi(δ1,Z) = qr , e −πi(δ2,Z) = r −1Òe ´ÊÐÐØØq =<br />
exp(−πi(ρ,Z)) = q 1/2 r 1/2 s<br />
ÒØ<strong>×</strong>ÒÓØØÓÒº<br />
m −8nm)ºÌÖÐ<br />
r l s<br />
ÛÖØÖÓÓØα[n, l, m] = nδ 1 +(−l+m+n)δ 2 +mδ<br />
ÝØØÖÖÐ<strong>×</strong>ÑÔÐÖÓÓØ<strong>×</strong>ºÌÝÓÒÓØÒÚÓÐÚØÑÒÖÝ<strong>×</strong>ÑÔÐÖÓÓØ<strong>×</strong>ÓØ Ö<strong>×</strong>ÛØÓÒر1Ö<strong>×</strong>ÝØØÓÒÓÐÐÐÑÒØ<strong>×</strong>ÓØÏÝÐÖÓÙÔÒÖØ<br />
(Z)¸ÐÐØÖÑ<strong>×</strong>´ÒØÜÔÒ<strong>×</strong>ÓÒÚÒÒØÔÔÒܵØØ<br />
3<strong>×</strong>ÒÓÖÑ(2l <strong>×</strong>ÑÔÐÖÓÓØ<strong>×</strong>Ö(α[1, 1, 0], α[0, −1, 0], α[0, 1, 1])ÒØÏÝÐÚØÓÖ<strong>×</strong>ρ=α[<br />
ÃÅÄ<strong>×</strong>ÙÔÖÐÖºÓÖÒ<strong>×</strong>ØÒ¸ØØÖÑ<strong>×</strong>Ö<strong>×</strong>ÒÖÓÑÏÝÐÖØÓÒ<strong>×</strong><strong>×</strong><strong>×</strong>ÓØ<br />
¾ºÁÒØÜÔÒ<strong>×</strong>ÓÒÓÖ∆ 5<br />
1Ö<br />
ÒÓÑÒØÓÖÓÖÑÙÐØÓÜØÖØØÖÓÓØ<strong>×</strong>º<br />
ÛØØ<strong>×</strong>ÑÔÐÖÐÖÓÓØ<strong>×</strong>ÓG (q 3/2 r 3/2 s 1/2 , q 1/2 r −1/2 s 1/2 , q 1/2 r 3/2 s 3/2 ) = q 1/2 r 1/2 s (qr, r −1 , sr) .<br />
ÆÓØØØÛÒØÓÔÙÐÐÓÙØÒÓÚÖÐÐØÓÖÓq (Z)ºÓÖÑÐÔÖÓÓÒÚÒÝÓÐÐÓÛÒÖØ<strong>×</strong>ÒÓÒ<br />
1/2ÒØ<strong>×</strong>ÙÑ<strong>×</strong>ÓØ<br />
3<strong>×</strong>ÝÑÑØÖÝÛÔÖÑÙØ<strong>×</strong>ØØÖ<br />
1/2 r 1/2 s<br />
¿ºÌÃÅÄ<strong>×</strong>ÙÔÖÐÖG 1¸<strong>×</strong>ÈÖÓÔº¾º½℄ºÌÖÔÖÓÓÑ<strong>×</strong>Ù<strong>×</strong>ÓØÒÓÒ¹ØÖÚÐ sµ<br />
1<strong>×</strong>ÒÓÙØÖS ÖÐ<strong>×</strong>ÑÔÐÖÓÓØ<strong>×</strong>ºÁØ<strong>×</strong><strong>×</strong>ÝØÓ<strong>×</strong>ÓÒÐÝØδ 1<br />
(Z)´<strong>×</strong>Õº´º½µº<br />
↔ δ 3´ÓÖÕÙÚÐÒØÐÝØq <strong>×</strong>ÝÑÑØÖÝÒØ∆ 5<br />
ÆÙÐÒ³<strong>×</strong>ÖÙÑÒØÓÖG ÖØÖvΓÔÔÖÒÒØÑÓÙÐÖØÖÒ<strong>×</strong>ÓÖÑ∆ 5<br />
½<br />
∆ 5 (Z)º<br />
α[n, l, m]ØÓq<br />
n<br />
q<br />
)ºµÌÙ<strong>×</strong>¸ÓÒ<strong>×</strong><br />
−πi(δ3,Z) = sr .<br />
exp(2πiz 1 )¸r=exp(2πiz 2 )Òs=exp(2πiz 3<br />
n r l s m = e −πi(α[n,l,m],Z) ,<br />
2 1<br />
↔<br />
2 , 1 2 , 1 2 ]
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