The Standard Model Lagrangian Abstract The Lagrangian for the Standard Model is written out in full, here.

Size: px

Start display at page:

Download "The Standard Model Lagrangian Abstract The Lagrangian for the Standard Model is written out in full, here."

Jonathan Dalton
6 years ago
Views:

1 Th Stn o nn Atct Th nn fo th Stn o wttn ot n f h Th py noty of th ppoch opt h th p ny of th fonc pc Anoo to th tton n th 9 th cnty n whch xw nt th pcnt cnt t n th f w fo ctont n o to tn ch conton w n n ot th ytc tct of th qton th ht ntno py th coponn o n th pnt tton th ytc tct tht tht wth th ncon of th xt t th fon pc fcto nfcnty y poyn th ytc tct th nn y wttn n tnty o tnpnt fhon Two fo fon pc w op h: th hypcoo n th C Th Stn o tf nc pc c wthn n nopn nzton of n-- tho tht po oo fo ft xtnon n ptc th kw cto op fo ft pncp n-- nn Th Stn o n ntnc of n-- yt whch y o xtn ow to nc oth cn yt n on fth th tton ntcton Fnnty t thoy of pn ½ fonc tt n th nfnc of n- f whch t y pn oon Th f yty of th ntcton okn t th tt pc wth th c tnn ony yty Th okn yt to xt c o ot of whch th f whch ny cop to th f w Th ntcton of th n fon f cn tn py y th qnt tht t tn n th f A hown ow th ny ffcnt to po tht th copn t of th kw typ oth th ton n th cton of th f to no w c ot n t ow th pct to th notton to op ow th nn fo n-- thoy y wttn! A ) ) ) ) k F F ) A ) A ) ) )! / An nttn poty not fth op h of pn th nn ck to q oot y kn of fon potnt to nt th f Th opnt h n c n noth wtp t not fy op h t q n ntcton tht pty-ytc whch t n coy wth th ow n th cton on th C Thoh th Stn o tf not pty ytc t t po xtnon to n ntcton tht wh pty okn yty Th n tht f qy n n wth th S-Sw o of ntno phyc n- Scto Th f A oct wth yty op y wttn n t of of th coponn ) : ) A A n ) f ch th xw f n nkowk f th kntc ont P of tt ch t cnonc ont n t y P p n th potnt A th pct fo t p ) A ) p A t p A

2 wh th pop t of th tt ch Th ton nz n ty coont f to p P A Thoh th Eqnc Pncp thy nz fth to oc coont f fo c pct Fo n- f wth op n coponn ton ho wth th c ch pc y ch co-cto n th p poct pc y n nn poct n th cto pc of th p P A n qntzton th cnonc n kntc ont pc pcty y th ony t n cont t D A thoh th coponnc p! P! D Th to th foown pntton fo th ch! Th ch opto tn n nto nt-tn t coon pctc to noz th ch nto y xpcty nn ot wht copn contnt no o tht on y thn wt nt Fo p op th w ony on copn wh fo -p op th w ffnt copn fo ch fcto y connton nt ny chon ch tht! thoh w y qy w th xt! hn n o n th fnton of th copn Th f fo th Stn o tht fo th op S ) )) y connton t wttn A Th ch nto tho of th con op ) S ) S ) wth th pct ch opto of th coponn ) ) ) Th cotto fo th n ) pcty ) k c [ ] / [ f / j k Th coponn tn fo [ j k ] jk wth jk ] c c c n [ ] f c [ ] [ ] [ ] [ ] copty nt-ytc [ ] [ ] [ ] [ ] [ ] [ ] Th f tnth fn y [ A A ] F A A wth th coponnt n xpcty y

3 k k k k j / k c / c c c c f Th f nn n y k wth th op tc fn thoh th ch nto y k k k j F F ) k F F )!! /!! ) ) ) k j j An jont nnt tc on tfyn th popty k ) k ) whch p k [ ] w) k [ w]) ) k ) / k ) / Th ot n non-nt jont nnt tc fo S ) )) t tk on th fo jt n po tht th ) o othoonz wth pct to th oth f Th ccoph y tnfoton of th fo w whch w not ffct th nyn Th copn coffcnt cty t to th op tc yn t npnnt coponnt Expcty th nn tk th fo! / j c / )!!! / j c n th cc f thoy th op tc to contnt thoh th pton not ncy nnt of cc thoy n th qntz thoy th qnt of nozton foc on to now t wth c pnncy n n c pnncy f to th oton t whch th pont-k oc pnt y ntctn qnt f po n cttn xpnt n ffct th tc co pnnt on th tnc fo pont-k oc kn t n fct) fncton of poton tht tn tow contnt yptotcy n t of th co ton of th copn to th tc th tnt nto tx nozton o qnty) oct wth th cn of th f Fon Scto Th fon fon n th foown S ) S ) ) cto 6) ) ) ) ) ) ) ) ) ) ) 6) coponn to ft Poton ht p Qk ft Ant-Down Qk ht Ntno) ht Ant-pton ft Qk ht Ant Qk ft pton ft Ant-Ntno) ht Down Qk ft Ant-p Qk ht Ecton pton f cocty to cton n ntno; nt-pton to poton n nt-ntno Th two ) cto nt n thfo o not ptcpt n ntcton n thy h nonzo Th not nc n th Stn o t thy w tn h fo th k of pcty Th copon to th ht-hn ntno n ft-hn nt-ntno Th qton

4 whth n how th cto xt w opn ptcy wth th coy of ntno octon nctn th xtnc of non-zo ntno Ao c th ton cto h zo ch t tn ot tht th o wy to now th wth thn qtn ntno wth Dc f Th nc th poty of jon f o conton of jon n Dc f Th o -fo ncy of th ch pct coponn to wht c nton So th pct xtn to qnt non two oth t of ntno n wth th foown pcnt { Ecton p Down } { Ch Stn } { T Top otto } Th nton y ntf y th ch ntt whch fn th no o of ntcton wth th f Thy y o fn y th ntt fn th no o of ntcton wth th f Th f tf o h chotoy of pntton Th n jt nton f to th ntt Th cpton ty to foow f to th ch ntt Snc th f oct wth S ) non-n n nc pt of wht w c ctont thn th coponn f qton non-n n nhoono contnn on th ht-hn of th qton onn oth ctc n ntc oc contct nty fo th f ntc onopo oton cn th n o fo th cc thoy to contnty qntz t t f fo no Th on noy tht occ cty oct wth th ft-ht yty of th S ) cto f th xt ntno cto nt th qnt tht th noy nt nqy pcf th ) ch p to nt whch y ntf th qnt Th pct n o fo th hypch wttn n t of th t ) ch Th nt opt n th tn tt th o 6 t th f th xt ntno cto nc thn th noy o conton ow fo p to pt ) cto o conton thof) th con n oct wth yon n Th pct pt twn th Dc pno n t conjt pcty nto th tt n nt-tt cto ) ) ) ) ) 6) 6) ) ) ) ) ) Th yt of th Stn o o nc SO ) S ) S ) whch ptn to th chn n th oc pct f n xp n th copoton pcty fo ht n ft n th f hn tt Th fon occpy th cto ) ) S ) S ) ) S ) S ) nnt 6) ) ) ) ) ) ) ) ) ) ) 6) Th tt-nttt pttn not nq oth pttn po t th potnt nt tht th Dc pno n to oy tc ) cto n th foown pn 6 T ) ) T tht oct th ) ) ) ) ) ) ) ) ) ) ) 6) Th cont ot th tc ppy h n cc f thoy th fon tc contnt t nozton n qnt f thoy now t wth c pnncy tht k th

5 tc pnnt on th tnc fo pont-k oc kn t n fct) fncton of poton tht tn tow contnt wy fo th oc Th tnt nto th nozton fcto oct wth fon cn Th fon tc not nnt ) ) n th op ct n pty ytc wy n topct th y n nt fo pty n okn yty wth th ntcton cty n ytc n pty Th ypcoo w h opt th tt nt-tt copoton xpn th oct t pc n th foown poct { } { } { } { } { } z y x w t w w wtch o to th 6-t pntton whch tt t to fcton ot th nt tct contn wthn ch nton of th fon pct tht n tn tony t of n nyn n ) SO Th coponn ntty opto w not y z z y y x x w w C P S n th foown tno poct w wttn ony poct wth th ntty opto ott Th fo ntnc ) C S Th ft two fcto { } { } ccont fo th ) SO copoton wth th pct nnt { } ) { } ) th pct to th th Dc tc th fo ) ) wth th P tc n th fo ) Fo th w t 5 Th th y pntton n t copon to th copoton of th Dc pno nto y pno foow n n n notton ) ) wth nc y

6 Th th fcto { } ccont fo th ctowk cto who yty op n y ) wth th -fo con op S ) ) Fo tt tt th ffct th foown ) SO) copoton { } ) ) ) ) ) ) tn n opn nto qpt ) ) ) ) n n to th foown opn of th tt fon tt nto ) SO) ) S ) ) ) ) ) ) ) 6) ) cto th pct to th th S ) nto wh Th foth fcto { w x y z } n th th ) ) ccont fo th S ) copoton wth th nnt S ) nto co x y z ) w wh Th 6 x x z z y y ) nto co z y y x x z ) z x x z ) y x x y ) y z z y ) x x z z x x y y z z wh x x y y z z w w 6 th yon n opto n ton fcto of fo ft connc) Fny th t fcto { } ccont fo th nton ncy No thotc wht ncy n n to th ptc pntton t t th ot connnt wy to wt ot th tt nt-tt nnt of th fon pct to th Dc pno Th xpct nnt th { x y z} w ) ) ) ) ) 6) { } { } { } { x y z} { } { } w{ } { x y z} { } w{ } Th n to th conjt pno foow

7 ) ) ) ) 6) ) w{ } { x y z} { } { } w{ } { } { x y z} { } w{ } { x y z} { } Th fon pt of th nn / A ) Expcty n t of th fon tc th co A ) ) / Th C Th ppnc of ht no to n th pntton of n copoton of ) n th ppnc of th yon n n tony t o fnnt o ho py y th two opto Th nt n th tn o to t th hypch pct no conton to o ch noy pnt n th f thoy A hown y A tnn 996) {Ano n qnt f thoy Cnon P Oxfo} th n contnt D! ccy tf th Poon ckt ton c { x) y) } f c x) / x y) t pon qntzton cq n xt t coponn to wht known th Tn Anoy n ptton thoy [ x) y) ] c 5! f c x) / x y) T { }) / x y) A!! Œ tty th qnt fo o co own to th conton tht T { }) 5 k j Tht th cc conton of th wht o ch of th ft-hn o ho p to th coponn cc conton o th ht-hn o n th nc of th ht ntno n ft nt-ntno cto o qnty f on tht th ch ) th contnt nqy n nton-nnt ch p to n o c ow ythn chn whn th xt ntno cto oht n Thn on o fn tht th yon n ow Th ot n oton n conton of th yon n n hypch o qnty) th ht opn X n ptn ot th ht opn w y wt own th fon pct n th S ) ) S ) ) S ) S ) copoton X ) ) ) ) ) ) ) ) ) ) ) ) thn cy tht th pt copoton fo n ) nto th fon c T fo th ) X ) X ) ) ) nto ) ) ) ) wht y thn cop

8 ) ) ) ) X th thn th C nnt n two pn opto X X ± ± t w tn ot tht th -fo nton ncy w t to th nto o tht th f pct w cont of th thn jt fo Th w to th ocoo ttc pct ow Th wht n nnt contnt wth th nnt of X n ht-hn no S ) of opn S ) wth th ncon S ) S ) ) X Th ppnt nc of co thn xpn t t n pt y n th pty oton of opn okn yty Th ky pont of nxpn ty tht tow th cton ) th zo o of th ctowk yty kn o th pty-ytc o ) th -pnncy of th fon tc n th nc of o pty-yty tnhn t n contt to th n tc whch oth -nnt Th ot nfcnt ty tht wo f pty-yty to t th of ntcton tht th fon cto of th nn wo fcto nto fo n y / A ) ) ) ) A wh th f tf tt th ct oct wth fon potnt Th coponn t fo th ) wht ) ) ) ) 6 6 whch th con C nnt n th o pn opto 6 ± ± ± Th contnt wth th nnt of 5 6 n hypcoo op S ) ) Th o copoton x wth th oc yty op SO ) th ) X SO ) copoton Th ) ) ) ) ) ) ) th xn of th two cpt qpt ) ) ) ) wo copon to th fnnt qpt wthn S ) ) ; y th ) X SO ) qpt wo copon S ) S ) S ) S ) n wthn ) ) pcty to ) ) ) ) o S ) S ) S ) S ) S ) ) Pty nttwn wth th ntn yty pc n to n ffct copoton of th fon cto nto ffct ht n ft pc ) )

A conqnc of th pty y ncpt y th 5 pn opto Thfo to pcfy th ) on n ony th tt SO pc nt of n th poct { } { } { } Atnty on of th pn opto y nt n fo of th pty opto 5 Th nn opto X X c Th conton of th ± of

9 A conqnc of th pty y ncpt y th 5 pn opto Thfo to pcfy th ) on n ony th tt SO pc nt of n th poct { } { } { } Atnty on of th pn opto y nt n fo of th pty opto 5 Th nn opto X X c Th conton of th ± of th opto w poc th ch ntt of ch nton A c t th -ny ntt of n ocoo w xt fo of th of ch ocoo tpt Th to fcton of th fon pc nto th ocoo ttc oct wth ) X n th Fon C oct wth ) Th nnt of th nt n n th foown t

10 nt X c Th tpt c n ntnc of th pntton of S ) wth n y ntf pcty wth th coo nt n cyn Th ot n ntnc of th pntton of S ) wth X Th w tn ot to th chcttc of th ot whch thfo y ntf th fnnt ch coponn to th nt Pty t to th oth pn opto y th ton 5 n c) n th on pn opto tht chn wth pty whch ffcty pnt th pty opto of th conton of th oc pct f n ntn n Thfo w w pc th opto y pty p n 5 ) n wt th cp wth c p { } Th ffc to th fn th 6 coponnt of th -coponnt fon pno o othw 6 copx coponnt wth conjcy ton opt th tt ppoch xpn fon pno n th fo cp cp c wth th conjcy opto n ch conjcy opto & tn th coponnt w opt th foown connton & cp c p n c cp cp p cp c p c c cp c p wh w th n of th pct t fcto p n p) n th p to not n Tht ) p ) ) ) ) ) ) Th chcttc of th o tt n n th foown t tt c < Ant-tt c > ptonc c yonc c o c ht p n c) > ft p n c) < Th pno coponnt fo ch fo n c ) c) ) ) c ) c) ) ) c c c ) c) ) ) c ) c) ) ) Th ffct of th Dc tc on th n y th foown cp p cp cp cp cp p cp 5 T cp p cp cp p cp

11 Th ffct of pty n t- n y ) t) cp t) cp 7 ) t) cp p t) c p n t of th C th nto tk on o nttn n n fo Th ) nto x th cton of th ht opn n yon-pton n n h th foown cton c c c Th S ) cto ony ct on th nc wth th foown t Fny th 6 c c c c S ) cto ony ct on th c nc wth th foown t c c c c c c c c 5 7 c c c c c c c c c c c c c c c c Th nto pfo xchn whn th two qt ff; wh th nto ; 5 n 6 7 pct pfo xchn on c c n whn th qt n th pct p ff Th nn nto on wth c c c poc th n pct of th 5 qt fo th 5 Scto Fo th cpton n th n th nn cton w w th hypcoo Th fon n th foown S ) S ) ) cto: ) Th { } w thfo fo th pc wth th coponn ntty opto P fn fo n wth th foown copoton w ~ Th cton of th op nto on th cto th P Th c pt of th nn A ) ) ) > ) A Th f y copo nto po fo y wtn Thn Φ ~ Φ Φ ~ /

12 wh ) Φ Φ Φ xp xp ) Th ffct of th pcfc pntton to oy th c tc ) Φ Φ Th cto thfo th cycc cto ntn th pntton ) thfo wttn A ) ) ) ) / A An potnt popty pct n th notton tht th tc nnt ) ) Th nn y Th cont n ton to th fon n tc ppy h Th cc f thotc nt of th c f tc w contnt t n nozton n qnt f thoy t co c pnnt ffcty kn th tc fncton of th tnc fo pont-k oc tht tn yptotcy tow contnt wy fo oc Th tnt nto th nozton fcto oct wth cn 6 kw Scto n th thotc tt th th t w-op pt of th Stn o n t of wtn t n ntnc of n fo n n th ntcton twn th fon n c f to n y nn tn copn of th fo / ) n o to p nnc n fo th nn to n tn th copn ) t tfy th foown conton )) ) ) ) n nty tnfoton A A tn th n po fo w fn tht ) Φ Dcopon wth pct to th { } Φ ) ) Φ Φ w fn ) Φ ) Φ Φ Φ Φ Φ ) y pton th tn copn whch n th qtc n qtc t not pnt Thfo Ftho th tcty conton p tht Thfo w y wt ) Φ Φ Th th ntcton nn kw t / ) Φ Φ ) wth copn who copoton wth pct to th -fo ncy xpcty wttn Φ

13 n F n w w n n n n n n n N E ) x x y y z z ) D ) Th th ot n copoton wth pct to th nn tht h nnc n th S ) cto y ppoton n N Th t h n tn h on wth th ht ntno cto fo th k of nty n xtn on of th Stn o ntno h to ncopot n o fhon Th pt pton tht th ht-hn ntno n th t py no c of t ntty t wo ntct wth th n thoh ty t th t nn n th t n of th ntno wo n tht t ty wo ffct to w 7 n-- nn Conn th t w fn tht th Stn o n ntnc of th n n-- nn whch y fn y / wh ch tht! A ) ) ) ) k F F ) A ) A ) ) )! [ A A ] F A A )) ) ) ) ) ) On potnt qf woth notn h n t of th ntty of th ht-ntno cto o n copn ow th tty n to nt of th S Sw chn Spcfcy th cton of th op on th cto w w w w ) w w t o tht t of th fo w w ) y nt nto th nn wthot otn nnc Th kw copn w tty now th oth th ft n ht hn coponnt wth th thy n to tot ntno tx of th fo w w ) ) Th nt of th ntno pno cn thn pn th p twn p Dc to p jon n ywh n twn pnn on th t z of kown of th c Th Stn o hypothz tht th no fnnt nt t thoh ntcton wth n c ny f c th n ffct th n th c ctc whch p o of th coponnt of th ctowk foc Th ony nn coponnt tht th c tnpnt wth pct to th ctontc foc whch conton of th n oon Th conton th ony on tht pty-ytc Th c not tnpnt wth pct to th pty-ytc coponnt of th ctowk foc Th coponn oon thfo h t n whch kw -n coponnc) ffcty tnt nto Th photon n Th tn f qton ccy) th xw-

14 Poc qton n ffct th coponnt of th co th ton coponnt of th pct xw-poc f Fo th fon th ffct of th to tnt th fon twn ft n ht hn o Th ffct z-zn pcy tht whch chctz th ttwn of Dc ptc n ffct th fon tn t ht p t n ch j pth c of th p tnton tht t oton tht of ptc Th tnth of th ptc ntcton wth th tn t t of ntt to not tht th hypoth tht th c h ctc not ony ont wth xw t cnt th of h nt ttnt of cc ctont t h n wnt fth n fy c wht n on n known An n- f n th noton of non-t ctotton nfcton xn n Th potnt h n wh ) Th h y n wttn n po fo Φ Th nt th th of yty of th c th oton oon n hn th on nn of fo fo th c f Th n ttn of th ony tn p to n o Ech ttn fn ffnt c tt t tht th of fo fn ch tht fo th c tt tht fn th wo A conqnc of th tnfoton th w non-zo no n th ctowk pt of th oon pct hn oon h ony of fo; t n tt thy h th Th of yty co th pct of fo Th photon how n wth ony t hcty o wh th n nttch c f Entt oon Stttn th c xpctton nto th c pt of th nn th nc of tx fo th oon ) A ) ) A A ) A A A wh w wt th oon f cocty A A n fn ) )

15 Th th q of th tx Th ony non-zo coponnt tho oct wth th ) ctowk cto wh w fn tht ) ) ) ) ) ) / / j j j j j j Th to th foown copoton ) ) A A Fo th w fn th pct ntt n th oct n ± A # Th ffct nn co f th tn wttn n po fo th t co Th wk xn n fn th n twn n 9 fo whch tn Thn th two nt oon f n th to of th two n y wttn co n co n co A Th contnt tty t to th F contnt 5 669) F y F Th xpon fo th photon f A y copn co n tht pty npnnt Thoh th on fn F Œ n n t of th fn tct contnt 6 7 Fo th on t ft o tt th n h o cocton fn th to ch o co to th xpnt 9 Of ptc ntt tht th tc of th ft-o oon tx y ny q to th c xpctton of th

16 Th f-potnt o to n ntt on wth th ntt tht t o nto th ctowk f Th kntc n potnt pt of th cto co ) ) Th ft t y xpct of c f Th con t y ) ) tn n tot ) non th ppnc of Th ow on > 6 cnty known t y hh t th t of wtn) Fon n th foown w w th pojcton opto z z y y x x w w D Th t co ot of th kw cto nc th th pc wh th t twn th ft-ht ttwn of th fon f Expnn th f w y wt Φ Φ Th kw t y thn c to ) ) Φ Φ / wh Φ n n n Dfnn th pojcton opto th fon tx y onz pty o t pct cto D D E N D n t of tc nty o nton pc n nton-onz tc E N D t c whch xp n t of th n wth typc tt n y

17 56 ± 99 ± 5k c 5 ± 5 99 ± 5 7 ± 6 7 Snc th Stn o ony) tht th ht-ntno cto w nt o non-xtnt th ntno n w to zo Th oth n f pt ow t of ntt to not tht th tc of th pton tx tf n ppoxt ntty to tht oon tx t wth n nttn ton T ) wh th fn tct contnt t ppoxty /7 of th c xpctton Th copoton to th ntt of th fon wh D D ) D D) Th to th xpon of th kw n th npc D D N E D) / 6 Th ntcton n CK tc Th tnfoton tc o not py o wy Th conon to th ntt ffct th n of th nn non fon wh of th tnfoton tc w n n th chn to th n th fon pt of th nn co / A ) A ) A ) ) A Th tnfoton tx no th pojcton whch cot wth th nto t o th pojcton D whch cot wth th nto fo ) n S ) t not tho fo S ) Th nto cot t not Expcty fo th coponn tc w h D D ) Th D D D D ) ) ) Th tc tht fo th th Ko-Coyh-kw CK) tc Q Th pton cto tx f to th k-nkw-skt NS) tx thoh w w f to oth cocty n th n CK Th t of th tnfoton D D ) D D ) ) Q Q whch chn th nto to wh ) )

18 n th of nt n y ) ) ) ) Q Q f th ntno h thn ty n y fn to whch w thn c th ptonc CK tx Othw f ht-ntno n ft nt-ntno) cto th tx w non-t Snc ony th nnc ppnt th tnfoton twn th ch n ntt y con to no nothn o thn th two tc y connton on tk Q Expcty th tnfoton twn ch n ntt fo th ft-hn coponnt of th f thn wttn t t t c c c Q t c t c Th foown tt on th qk xn tx xcn th ph nfoton) Q ct n Tn X:hp-th/56) who h popo thoy ccontn fo th nton tct n xn ton who py ton tht th fon tc D N n E ch of nk n fo coon fo y th nnn of t of pt of th) Expnt tt fo th pton xn tx n xcn ph nfoton) ct w: Th thotcy Q whch ft w xcpt th o ntno n 5 Th ntcton wth th Entt oon F Th CK tc ffcty co pt of th nto jt hown Th ffct cononnt wth th cton of th oon f to ntt whch wok n tn wth th cton of th fon f Th CK tc ttch to th copn of th f wh tho of th A f n nffct Th fo thfo th ony f to t ntcton twn th ffnt nton of ntt t ony y th ntcton tht th tpcty of nton n cty o Th of co to n nttn qton n t own ht: 96 owht o n fo th tot n of fon tt p nton) wh wo who ot o nt Co th th nton tht t? h ptc cttn xpnt

19 t th z of th cto t y th CK tc to nton thy h nothn cty to y ot th xtnc of oth CK cto not ttch to th known nton o n t nton An nttn hypoth n th tht th o fo S ) y not h n tht f off th k Php th copoton n n th qk-pton S ) copnt y copoton fo th CK cto Th on nfcnt tht t pow of Th pow of tct y n wthn n nton tony t of n nyn Cffo t ny ony th th thn p o -p op tht to pow of pttn n th c pntton Of th p op ony SO ) h th cpty of pocn ch tt pc t h 6 ) A tx tct nty oct wth th -non Dc oct wth SO ) ow to t coponnt q non o 5 tton Extnon Th o ccont cnnot y con copt nt th f ffct of th tton f oht n w Thoh t not tcty pt of th Stn o th fct n tht n n th nc of ty o n wk ty) on wo t k to ot to n non-ctn coont o n non-coont f Thn th fw not ffnc not th t of whch tht n xt fcto pp n th nn n ptcpt n th o n fo tht w ncont Th ppoch opt h to tt ty thoy fo oc Poncé yty Th cnnot n- thoy nc th Poncé op not n -p ch copct Oth noty Snhy) h pont ot tht nc th fon k th ) wo yty own to SO ) n t th pnnc on th Cffo n fo y th Dc tc thn ty y t nt pontnoy okn yty wth th n n th oton- f oct wth th yty kn ow fo th foown w w opt th ppoch of ttn th n th f oct wth th tnton nto of th Poncé op Thoh th thoy y not n- thoy t ht yt nz thoy n whch th f ony t fnctony to th f tnth jct to th qnt tht th nn y ton of th fo - // / F / A n tht [ F ] Th w t y th f qton n th foc w w t nt nto conton w non t tno nty [A ] 7 - F 7! F! / t th qton of how to n th f no oc Spct Syty op n ty Th f op n t h ton nto fo th oc pct yty op - /

20 SO ) : p ); ) Snc SO ) not copct no n -p n jont-nnt tc o t c to k p ) k ) Fo th oc pct yty op th n y [ ]! [ p c [ p c c c c ) c ]! cp cp ) ]! p p ) [ p p ] c c c Th y pf y wtn th n ptz fo n t of n nt-ytc tx & n cto & ) & p yn th ckt & ) )] & & & ) [ Th n ton fo th ty f to th f n th coponn tnth n y A & p F p Th tton pt ony ct cty on th fon cto Th p nto o not ct cty nywh thoh t ht hn y n nc n th t opto y th pntton p ow) Extnn th on y fn th ch opto y J Thn th cont t t co p Fo pn ½ Dc f th ontz nto jt th pn opto! wh n ptz fo th tton pt of th f y th wttn A & ) F ) wth c pt of th cont non th n of th f o on th wth th coponn cnt D whch jt kntc ont & & & & & & & & Th tton-- nn th th pn t th nn pt of th cton y wttn ot wh c 6 Œ c A ) ) ) ) A ) A ) ) ) /! k F c c F! ) 6 Œ An xt t non th coooc contnt whch pt of th contton fo th tton f h n nc

21 On of th cnt t of th thoy of pncp n tht whn th tc pct tc n f con nto n tc h ) k A A ); h ) k A ); h ) k ) o qnty h D D ) ; h D ) ; h ) k ) thn th coponn Entn-t cton w copo nto c c! c / E h) k F F ) k f! f c Œ 6 whch po coooc contnt t f th tc to whch ont to n tht th copn ) xt t coponn to th t of th tc pp k ny t Ftho th xt coooc contnt t o co thot th ty on fc wth th fn tnn po of xpnn th ncy nky poty of xty yt non-zo coooc contnt n ot of th xt t Fth t on th tt not p ot h Th f to nt tx wth th n ) Th qton of t ntty coy t to th pton of th pcfc fo fo th oc pct op n n on cn ony y o n n -non nfo tht th oc yty op n) Th tcton to SO n ) oppo y to SO n ) o SO n) ont to n pct pton of ctn of cc c ckon nto th nyn pct n th nt of th tc pt of th ckon Th ntty thfo y nftton of th o n po: th nt po Fo th f co th tc n t Not tht th tc o n ony pp n th pc wh th o nn poct o n fo pp A y n th nn poct oct wth th fon no th Dc jont n tk on th xpct fo ) T T T T

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

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