УК гд а Уж × в

ÒÖÔÐØÈÓ××ÓÒÖØ×ÝÓÑÑÙØØÓÖ׺ÌÕÙйØÑÒÓÒÐÓÑÑÙØØÓÒ ÔØÖ½ºËØÖÒÌÓÖÝ
ÖÐØÓÒ×ÖØÒÚÒÝ
Ì×Ú¸ÓÖØÓÑÑÙØØÓÒÖÐØÓÒ×ÓØÓ×ÐÐØÓÖÑÓ×ØÓÐÐÓÛÒÓÑÑÙØØÓÒ ´½º¾µ
ÖÐØÓÒ×
[P
[X µ (σ, τ), X ν (σ ′ , τ)] = [P τ µ (σ, τ), P τ ν (σ′ , τ)] = 0 .
´½º¾µ
[α
ÛØ×ØصÒØÓÒÒ×ØØÓØÖÒØÖ¹Ó¹Ñ××ÑÓÑÒظ
k〉¸×ÒØÓÒÒÐØÝØÐÓÛÖÒÓÔÖØÓÖ×´××Ø
[α m µ , ˜αµ n ] = 0
ÌÖÓÙÒ×ØØ|0;
ÓÔÖØÓÖ׺ k〉ÛØØÖ×Ò ÒÖÐ×ØØÒØÓ×ÔF kÒÙÐØÝØÒÓÒ|0;
)¸n∈NÒÐÐÔÓ××Ð ´½º¿½µ
Ó×ÐÐØÓÖ×ÖÔÖ×ÒØÒÒÒØÒÙÑÖÓÒØÖÒÐÖ×ÓÖÓѺÌÓÚÕÙØÓÒ ÌÒØÖ¹Ó¹Ñ××ÑÓÑÒØÖÙ×ØØÖ×ÓÖÓÑÓÔÓÒØÔÖØиÛÐØ
Nº
|ǫ;
ÓÖÐÐÔÓ××ÐÄÓÖÒØÞÔÓÐÖÞØÓÒØÒ×ÓÖ×ǫ(k,
×ÒÐ×ØÖÒÛØÞÖÓÑÓÑÒØÙѸÒÓØØÞÖÓ¹×ØÖÒÚÙÙÑ×ØغÌÚÖÓÙ×ÓÔÖØÓÖ×
m 1 , m 2 , . . .,m n
m i
0〉×ØÖÓÙÒ×ØØÓ
∈
ÐÓ××ØÖÒØ×ØÒ×ÓÖÔÖÓÙØÓØÐØÒÖعÑÓÚÒÓ×Ô׺ÚÖÝÑÔÓÖØÒØ ÔÔÖÒÓÚÐÐØÛØÒØ×ÔÓ×ØØ×Ó×ÒÐ×ØÖÒº ÌÓÔÒ×ØÖÒÓ×Ô××ÙÑÓÚÖØÓ×Ô×ÓÚÖÐÐÑÓÑÒØkºÓÖØ
ÓÖÑ×ØÀÐÖØ×ÔÓ×ÒÐÓÔÒ×ØÖÒºÌ×ØØ|0;
ÒØÚÒÓÖѺÌÔÝ×ÐÓ×ÔÛÐÐ×Ù×ÔÓØÙÐÐÓ×ÔºÏÒ ÑÒÙ××ÒÒØÖÓÑÑÙØØÓÒÖÐØÓÒ×ÒØÖÓÖØÓ×ÔÓÒØÒ××ØØ×ÛØ ÔÓÒØØÓÓ×ÖÚ×ØØØ×Ó×Ô×ÒÓØÔÓ×ØÚÒغÌØÑÓÑÔÓÒÒØ×Ú ½¼
µ
τ (σ, τ), Xν (σ ′ , τ)] = −iδ(σ − σ ′ )η µν ,
µ
m, α ν n] = mδ m+n η µν
[˜α µ m , ˜αν n ] = mδ m+nη µν
P µ |0; k〉 = k µ |0; k〉 ,
α µ m
|0; k〉 = 0 m > 0 . ´½º¿¼µ
k〉 = ǫ(k, m 1 , m 2 , . . .,m n ) α µ 1
−m 1 · · ·α µn
−m n
|0; k〉,