Perturbation Series in Light-Cone Diagrams of Green Function of String Field
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1 Petuto Sees ht-coe Dms of ee Fucto of St Fel Am-l Te-So Km Chol-M So- m Detmet of Eey Scece Km l Su Uvesty Pyoy DPR Koe E-y Km l Su Uvesty Pyoy DPR Koe Detmet of Physcs Km l Su Uvesty Pyoy DPR Koe Astct ths e we ove the coesoece etwee Feym s ms sce-tme lht-coe ms wol-sheet y us oly th tel eesetto o fee ee fucto the fst qutzto theoy. We lso ote eel eesetto o etuto sees of lht-coe ms esc slt o of sts. Keywos : St fel theoy Pth tel Feym m. toucto 98 A.M. Polykov touce the th tel och to st theoy us sum-ove-sufces vewot tht mts mfest oetz emetzto cofoml vce. Howeve we cosee fuctol fel s fucto fel of ftely sevel vles eelze the ttol th tel fomlsm fucto fel to the ovel th tel fomlsm fuctol fel such tht we ote eet fuctol st fel theoy. Numeous clcultos e eque to ot the esult o cocete ocess y us Feym s ms o ee fucto of oe st eesete y eet fuctol of st fel ut t s ffcult ctclly. Othewse t s lso ffcult to clssfy Feym s ms hse fo et ume of vey ffeet ms e. But ll these comletes c e ovecome f t s covete to lht-coe ms 4. The ses tht Feym s ms sce-tme c e che to lht-coe ms wol-sheet e s follows: Fst t s tht fee ot fucto of st fel theoy c e ote two methos.e. the seco qutzto theoy t s 5 whee T Φ Φ s fee vcuum. O the othe h the fst qutzto theoy 5 D e & whee s the ectul eo the wol-sheet F.. Seco t s ossle tht fcto whch eesets sltt o of st tecto of st fel theoy c e eesse s fuctol wolsheet 5. cse of st s slt Coeso Autho Eml ess: yom@yhoo.com Te-So Km D e F. The ectul eo the wol-sheet
2 lm e t D cse tht two sts e o to oe equto coesoly s multle tel eo wol sheet s tue to F. Equto ws ove y us ee fucto eo efeece 5. The eltos sml to equto e mte covt fel theoy of st. Ou ols e fst to suest the eel oof metho wthout us the cocete fom of ee fucto ote lht-coe ue seco to clculte ee fucto y mes of lht-coe etuto sees wth eet fuctol eesete lht coe ms.. M of sce-tme m to lht-coe m et s cose the follow equto Fom ow we ll eess s. D tet ths equto wth esect to susttut the efto of we ot the follow: e e e D D D D D 4 The tet wth esect to D D we ot: e e e D D D 5 Now let s y tteto to the follow elto. D 6 ecto F. tel Reos wol sheet
3 D 7 f equto 5 s tete wth esect to cose equto 7 -fucto equto 5 s emove. Cose ths fct tel mesue em equto 7 s s follows: D D 8 O oe h the esult tet equto 5 s ove s s follows: e } e{ 9 whee e show F. Theefoe e D O the othe h equto cose the oety of ee fucto f the esult s s follows. lm Fom equto equto flly equto s ote. As show ove t c e kow tht the elct fom of ee fucto ws eve use oly ts efto oetes wee use. So we come to the cocluso tht ths elto oes ot elo to oly lht-coe ue. Ths fct s mott. Now the eesso of eet fuctol ouc Feym s ms sce-tme c e che to the eet fuctol ouc lht-coe m wol-sheet. To o so we ll ut equto of equto ste of. Fst ch } e e{ } e e{ D N y y D Dy D N F.. tel Reos Wol-sheet
4 4 Seco ch e D e lm D. h c e e lm e D Equto 4 cose equto s the eet fuctol of st fel we ty to ot. Ths eet fuctol ouces the lht-coe ms wol-sheet.. ee fucto of st fel et s cose the olem clcult ee fucto y eet fuctol 4 ote ove. Hee we ll f out wht k of sees the eet fuctol 4 ouces. oe to mke t smle we ll cose the ot fucto of oly oe st. 5 The tem wth the lowest oe etuto eso of equto 5 ves the ot fucto the seco-oe tem oes the oe-loo m. The esult s s follows: e 6 D 6 whee s the wee eo wol-sheet s F 4. f ot the hhe oe tems lke ths the she of the tems s ket the m the multlcty of the tel wth esect of ecomes out the -th oe tem the wee she whee fuctol tel wol-sheet s efome s ust che. Eess the ee fucto of oe st schemtc fom t s: e... } { 4... D M 7 F. 4. Wee Reo
5 whee { } mes the sum ove the eos of the wol-sheet wth ll ossle slt les. Fo emle the wee eo ossle u to 4 th s s follows: 8 Ths equto 8 eesses the lht-coe m. ke ths oe to ot the ee fucto of st fel we hve to clculte the fuctol tel o evey k of the wee eos cose coeso ouy cotos o the oues ths hs to e clculte wth cofoml m 4. Evey eo the equto 8 mes the tem of etuto theoy the equto out t s equl to the equto 7. Coclusos We ove the my elto e tsfom the Feym s ms sce-tme to the lht-coe ms the wol-sheet eel fom. By us ths we ote the eet fuctol ouc the lht-coe ms y ths equto ece the eel fom of etuto sees of ee fucto. The esult otte the e ws ote wthout eseclly us the eculty the lht-coe ue so we hve the osslty to tsmt ths to ffeet ue. Refeeces A. M. Polykov Phys. ett. B 98 7 B. Htfel; Qutum Fel Theoy of ot tcles sts Am-l Te-So Km So- m; Pth tel o eel Fuctol Fel v:.67 4 S. Melstm; Nucl. Phys. B M. Kku et l.; Phys. Rev. D
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