УК гд а Уж × в
УК гд а Уж × в
УК гд а Уж × в
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′<strong>×</strong>ØÊ<strong>×</strong>ÐÓÔº ÔØÖ½ºËØÖÒÌÓÖÝ<br />
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ÔÖÓÔÖÐÝÓÒØÖØØÓÑØÈÓÒÖÒÚÖÒصÙÐØÒØÓغÌ<strong>×</strong>Ô¹ØÑÑÒÓÐ <strong>×</strong>Ù<strong>×</strong>ÙÐÐÝÔ<strong>×</strong>ÙÓ¹ÊÑÒÒÒ<strong>×</strong>Ô¸ÛÒÓÙÖ<strong>×</strong>¸ÛØØÓØÅÒÓÛ<strong>×</strong> <strong>×</strong>Ô¹ØѸÛÓ<strong>×</strong><strong>×</strong>ÝÑÑØÖ<strong>×</strong>ÖØD¹ÑÒ<strong>×</strong>ÓÒÐÈÓÒÖÒÚÖÒ<br />
´½º¾µ<br />
X ′µ (σ, τ) = Λ µ ν X ν (σ, τ) + a µ ,<br />
ÓÖfºÌÒÛÑØÖ<strong>×</strong>ØÔÙÐÐÓØÓÐÓÒÒ<strong>×</strong>ÚÒÝ ÌÛÓÖй<strong>×</strong>Ø<strong>×</strong>ØÛÓ¹ÑÒ<strong>×</strong>ÓÒÐÑÒÓиÒ<strong>×</strong>ÒØ<strong>×</strong>ÖÓÙÔÓ<strong>×</strong>ÝÑÑØÖ<strong>×</strong>Ø<br />
(ξ)ØÓÓÖÒØÜÔÖ<strong>×</strong><strong>×</strong>ÓÒ ÛÖΛ ∈ SO(1, D)¸Òa ÖÓÙÔÓÓÑÓÖÔ<strong>×</strong>Ñ<strong>×</strong>f : Σ g → Σ gÓΣºÄØξ ´½º¿µ<br />
→ ξ ′a<br />
ÌÑÒØÖÒ<strong>×</strong>ÓÖÑ<strong>×</strong><strong>×</strong>X αβ<strong>×</strong>ÒÓÒ¹ÝÒÑÐÒØØÓÒ¸ÒÒÑÔÓ<strong>×</strong><strong>×</strong>ÓÒ<strong>×</strong>ØÖÒØ<strong>×</strong>ÓÒØ ´½ºµ<br />
<strong>×</strong>3ÒÔÒÒØÓÑÔÓÒÒØ<strong>×</strong>ºÌØÛÓ¹ÑÒ<strong>×</strong>ÓÒÐÓÓÖÒØÖÔÖÑØÖÞØÓÒ<strong>×</strong>ÔÒ <strong>×</strong>Ý<strong>×</strong>ØѺÍÒÐ<strong>×</strong><strong>×</strong>ÛÒÙÛÝÐÐØÒÔÒÒØÖ<strong>×</strong><strong>×</strong>ÓØÑØÖ¸ÛÒÒÓØÑ<br />
′µ (σ ′ , τ ′ ) → f ∗ X µ = X µ (σ, τ) .<br />
αβÒØÛÓÑÒ<strong>×</strong>ÓÒ<strong>×</strong> ÌÑØÖγ Ø<strong>×</strong>ÓØÛÓÑÒ<strong>×</strong>ÓÒ<strong>×</strong>¸ØÖÓÙÖ<strong>×</strong>ÓÒÑÓÖÐÓÐ<strong>×</strong>ÝÑÑØÖÝÐÓÐÖ<strong>×</strong>ÐÒ<strong>×</strong>ÓØ Ù<strong>×</strong>ÛØÓÒÒÔÒÒØÔÖÑØÖÒØÑØÖØÒ<strong>×</strong>ÓÖØÓܺÁØØÙÖÒ<strong>×</strong>ÓÙظØØÙ<strong>×</strong>ØÓÖ ÓÒØÛÓÖÙÒØÓÒ<strong>×</strong>ÒÛÒÐÑÒØØÛÓÓØÓÑÔÓÒÒØ<strong>×</strong>Ù<strong>×</strong>ÒØ<strong>×</strong>ºÌ<strong>×</strong>ÐÚ<strong>×</strong><br />
ÑØÖØØ<strong>×</strong>ÒÒÚÖÒÓØÐ<strong>×</strong><strong>×</strong>ÐØÓÒºÁØ<strong>×</strong>ÐÐØÏÝÐÒÚÖÒÓØ<br />
<strong>×</strong>Ò<strong>×</strong>ÐÒØÖÔÖØØÓÒÓØÔÝ<strong>×</strong>ÐØÓÖݺÌ<strong>×</strong>ÝÑÑØÖØÒ<strong>×</strong>ÓÖγ <br />
µ<br />
(4πα ′ )<br />
Dº<br />
γ ′ αβ(σ, τ) = γ αβ (σ, τ) ,<br />
∈ R<br />
a<br />
γ αβ → f ∗ γ αβ = ∂ξγ<br />
∂ξ ′ α<br />
∂ξ δ<br />
∂ξ ′ β γ γδ .
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