An action with positive kinetic energy term for general relativity. T. Mei

Transcription

1 An ton wt post nt ny t fo n tty T (Dptnt of Jon Cnt Cn o Unsty Wn H PRO Pop s Rp of Cn E-: to@nn tow@pwn ) Astt: At fst w stt so sts n X: 7769 n tn sn post nt ny oont onton n y X: 7769 w psnt n ton wt post nt ny t fo n tty Bs on ts ton t osponn toy of non qntzton s sss o sts n X: 7769 Bs fo of t toy Consn t tt f y w t t tnso s η () Dfn ( ) ( ) ( ) w s t R s offnts of otton: ( ) ( ) ( ) T Enstn-Ht ton ) ( EH R ( )( )( ) η () T osponn E-n qtons ( ) 8 T

2 ( ) ( ) T s ntts n tn npnnt qtons n qnt to t Enstn qtons n t stn E-n qtons T wn t onton () Un t onton () () s spf to t foown fo ( ) ( ) ( ) ( ) ( ) ( ) ( ) V V U U η η () In () t t t ony pps n n t s not t t n T stn E-n qtons n t onton () ( ) 6 V T U (5) 8 T (6) w ( ) (7) Bs t s not n t s not t osponn qton n t E-n qtons On t ot n w n po It sows tt os not po nw npnnt qton T st nn qtons

3 ~ s U ~ s 8 T (8) w U n ~ s n y () n (7) spty ( ) ( )( ) ( ) T non-post fntnss of t qt t of t t n T qt t of t t n n y () s non-post fnt Ts onson s oos fo t foown psson: [ ( )] 6 n wttn to t foown fo: w Γ ( ) ( ) Γ Γ () n δ A oont onton nsn post fntnss of t nt ny t n T foown fo s po: ( ) o () w s tt f w oos (9) () () tn ( ) () n t qt t of t t n 5 A op of ssttton n y (9) s ts post fnt Usn () n () w

4 δ δ () ( ) > > ( ) > (5) (6) Bs on (6) w fn [ ( ) ] ( ) 5 ( ) ( ) (7) Tn nt of (7) s n npnnt s spt fo t s yn s Conty w n otn sy t psson ( ) 5 (8) fo (7) An f t os not st tton f n (nows t) tn 6 T Cosy oposton 5 o t ppos tt n pss y n ft y ( 5) (8): ( ) ( ) w foown ontons < (9) onn t st fo n (5) s ts tn t: ( ) ( ) () ( )

5 ( ) 5 () T fo of n y () s so Cosy oposton n Bs on () fo n (5) w [ ( ) ] ( ) ( ) ( ) ( ) () () An ton wt post nt ny t fo n tty In w stt so sts n X:7769 on on t sts s tt t qt t of t t n n y () s non-post fnt t ny spn t qt t of t t n n ton ospons to nt ny of t syst f ts t ws non-post tn t ws w On t ot n t non-post fntnss of t qt t of t t n n ton s to t pnp of ton f [] On t ot n yt s on t sts n y w n psnt n ton wt post nt ny t fo n tty sttt () nto (5) (6) n (8) w otn t Enstn qtons wt t t () n t onton () wos ont fos no on wttn own In (9) t nt nt ny t n s K [ ( )] It s potnt tt w n po tt t ton 6 PK PK K K U V () (5) (6) n s to t Enstn qtons wt t t () n t onton () w n y () spy n t t ts ony pp n t t PK s 5

6 ( ) K Γ Γ It s oos tt t s not ny nt nt ny t n PK w tfo n s (5) to qntz tton f y os tos of qntzton In ts pp w ony sss t to of non qntzton T Htonn psntton As fst stp of t Htonn psntton w n nson oposton of sp-t nfo ts n z y t w-nown AD oposton: s ( )( ) (7) w o sn t fo of t foon fos w st s to not Un () ot () n (5) o n ts s n spy w (8) fnn o t ton (5) sstttn () nto (6) n onsn (8) w PK ( ) 6 5 (9) ( ) ( ( )) PK K 5 () n fo () w otn s t fntons of : stttn () nto (9) w ) 5 () ( PK ( ) 6 5 () o t o psson w n otn f onstnts: PK Htonn onstnt: ( ) ( ) PK Dffoops onstnt: ( ) ( ) PK PK onstnt: ( ) ( ) PK Aft zn qntzton t otton tons PK [ ( t ) ( t )] δ δ ( ) [ ( t ) ( t )] [ ( t ) ( t )] 5 () () (5) () ~ (5) n to f onstnt qtons fo w fnton Ψ [ ( )] t f qtons of oton of optos [ ( t ) H ] 5 (6) & ( t ) (7) 6

7 7 In (7) ) ( ) ( PK 5 H (8) A t ont fos of (9) ~ (8) otn y opt opt Rfns [] T On t n fos of n tty X:7769 [] ЛДЛандауЁМЛифшицТеория поля (Гостехизд ат 98) -