Strong Gravitational Lagrangian united into the Feynman Path Integral

8/3/2019 Strong Gravitational Lagrangian united into the Feynman Path Integral

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Z_AUUML OQ [AE [MLFEGMM_F

@rdh ugm fodpm oddb zrauuml oq N,N,[fb}rfa

Fod}u N, N, [fb}rfa Rf{{m{{hmlu d` ga{ krmeaoaiauq f{ f Sgq{aka{uXN}l Ndgl [fb}rfa) dlm d` ugm hfndr ugmdrmuakfi sgq{aka{u{ d` d}r uahm{) eame {}eemliq al Dkudomr 617?

zgaim pa{aualj KM_L al Jmlmpf, Gm zf{ dliq 51 qmfr{ die fle fu ugm gmajgu d` f oraiiaflu kfrmmr,

N}l zf{ odrl al 61;; al Udbqd fle zf{ dlm d` ugm kgaierml zgd zmrm mpfk}fume e}ralj ugm `arm odhoalj

d` ugfu kauq al Zdrie Zfr AA, Fu ugm fjm d` {awumml gm zdl f {kgdifr{gas ud ugm Ugdhf{ Nm``mr{dl Gajg

[kgddi al [u, Id}a{ fle urfl{`mrrme ugm `diidzalj qmfr ud ugm Ordlw Gajg [kgddi d` [kamlkm al Lmz Qdrb

`rdh zgakg gm zf{ jrfe}fume al 61=6, Gm rmkmapme ga{ }lemrjrfe}fum emjrmm `rdh Gfrpfre {}hhf k}h

if}em al 61== fle ga{ Sg,E, `rdh Kdrlmii al 61=7, F`umr f sd{uedkudrfi qmfr fu ugm Al{uau}um `dr Fepflkme

[u}eq al Sralkmudl gm zf{ fssdalume f{{a{uflu srd`m{{dr fu ugm ]lapmr{auq d` Kgakfjd al 61=1 fle `}ii

srd`m{{dr al 6105, Al 61:3 gm hdpme ud ]KIF fle gfe rmhfalme fu ]KIF }luai ga{ emfug, Al feeauadl gm

gfe gmie pa{aualj {uf`` fssdaluhmlu{ fu ugm Kfia`drlaf Al{uau}um d` Umkgldidjq) ]lapmr{auam{ d` Udbqd fle


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Lfjdqf) ]lapmr{auq d` Sfra{ fu Dr{fq) [k}dif Ldrhfim [}smradrm fu Sa{f) [ufl`dre Ialmfr Fkkmimrfudr)

KM_L fu Jmlmpf) fle Hfw Siflkb Al{uau}um fu H}lakg, Gm zf{ f [idfl @miidz '610?(6100!) @miidz d` ugm

Fhmrakfl Sgq{akfi [dkamuq '6105(617?!) f J}jjmlgmah @miidz '61:=(61:0! fle hd{u rmkmluiq f pdl

G}hodieu @miidz '6176(617?!,

Zgaim {uaii f jrfe}fum {u}emlu fu Kdrlmii) [fb}rfa zf{ dlm d` ugd{m zgd alemsmlemluiq ea{kdpmrme ugm P(F

ugmdrq d` ugm zmfb alumrfkuadl{, Al 6103 gm s}oia{gme al Fllfi{ d` Sgq{ak{ugm àr{u {mrad}{ fuumhsu ud

kdl{ur}ku f ugmdrq d` ugm {urdlj alumrfkuadl{ of{me dl ldl(Fomiafl jf}jm alpfraflkm, Al {saum d` padimlu

krauaka{h gm {ud}uiq em`mleme ga{ aemf{ fle zf{ mpmlu}fiiq srdpme ud om dl ugm rajgu urfkb, Ga{ lfhm a{

ldz almwurakfoiq mluzalme zaug ugm udsak d` pmkudr hm{dl{ al fii ugmar f{smku{, Al ifumr qmfr{ gm kdlurao}ume

h}kg ud alumrsrmualj ugm mwsmrahmlu{ zgakg emka{apmiq kdlàrhme ugm Zmalomrj([fifh(Jif{gdz }laàkfuadl

d` mimkurdhfjlmua{h fle ugm zmfb alumrfkuadl{, Gm gfe fizfq{ zdrbme fu ugm `drm`rdlu d` gajg mlmrjq

sgq{ak{ fle gfe kdlurao}ume al ahsdruflu zfq{ ud fii sgf{m{ d` ugm ugmdrq, Gm gfe f emms }lemr{uflealj

d` ugm `drhfi {ur}ku}rm d` ugmdrq) fl mlkqkidsfmeak bldzimejm d` ugm sgmldhmlf) fle zf{ fizfq{ al

kid{m{u ud}kg zaug mwsmrahmlu, [fb}rfa*{ zdrb zf{ kgfrfkumra~me oq f emjrmm d` alemsmlemlkm fle

`rm{glm{{ d` fssrdfkg rfrmiq `d}le mi{mzgmrm, Ga{ {uqim zf{ {ahsim) omfralj earmkuiq dl ugm gmfru d` ugm

hfuumr) ldu `drhfi o}u rmfeaiq kdhsrmgml{aoim ud f zaem f}eamlkm,

N}l zf{ fl d}u{uflealj imku}rmr, Uga{ ufimlu) kd}sime zaug ga{ {kamluaàk oraiiaflkm) hfem gah f h}kg

{d}jgu fùmr {smfbmr fu alumrlfuadlfi kdl`mrmlkm{ fle {}hhmr al{uau}um{, Ugm ia{u a{ udd idlj ud japm gmrm

o}u alki}eme ugm `diidzalj> Mrakm) Aufiq '*:;) *:0) *73! EM[Q) Gfho}rj '*:=!) [kgifehalj) F}{uraf '*:;!)

_mkdlurm em Hdradle '*:0!) Bqdud '*:7!, Ugm{m alpaufuadl{ mwumleme `rdh [gfljgfa ud Gmi{alba) alki}ealj

ugm [dpamu ]ladl, Ga{ umwuoddb{ f{ zmii f{ ga{ imku}rm{ fle rmpamz{ zmrm omf}ua`}iiq i}kae,N}l [fb}rfa zf{ f kdllda{{m}r d` hflq d` ugm jdde ugalj{ al ia`m, Gm mlndqme {baalj2 gm mlndqme

urfpmiialj2 gm mlndqme sifqalj ugm j}aufr, Ga{ àr{u idpm zf{ dsmrf) fle }lbldzl ud hflq d` ga{ kdiimfj}m{)

gm gah{mi` zf{ fl fkkdhsia{gme ofraudlm,

Al dremr ud gdldr [fb}rfa*{ kdlurao}uadl{ ud {kamlkm) f N, N, [fb}rfa Hmhdrafi @}le gf{ omml m{ufoia{gme,

Ugm `}le zaii om }{me `dr f sra~m ud rmkdjla~m d}u{uflealj zdrb al ugmdrmuakfi sfruakim sgq{ak{ oq qd}lj

rm{mfrkg {kamlua{u{, Ugm sra~m zaii om fehala{umrme oq ugm Fhmrakfl Sgq{akfi [dkamuq,

N}l [fb}rfa a{ {}rpapme oq ga{ za`m) Ldrabd) fle {dl{) Bml fle Jmdrjm, Zm {gfii fii jrmfuiq ha{{ uga{

ea{ualj}a{gme hfl,

N}iafl [kgzaljmr 'Ldomi If}rmfum!) _domru @albmi{umal


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[dhm d ugm lmz aemf{ ugfu A kfhm }s al hq rm{mfrkg zmrm

v}m{uadlme fu ugm omjallalj oq ugm {kamlua ak kdhh}lauq fle hq

[}smrpa{dr{ fu _qmr{dl ]lapmr{auq, Al hq Sg,E, ugm{a{ '?331! A

alurde}kme mz hdrm emufai{ alud ugm {fhm mv}fuadl ugfu

N,N,[fb}rfa gf{ zrauuml dl mv}fuadl ( ?,0,66 dl sfjm R;X,

@_DH [AE [MLFEGMM_F[ SGE UGM[A[ >

Zgml ugm uzd mv}fuadl{ frm kdhsfrme zaug mfkg dugmr) al ugm mv}fuadl

omidz al ugm rme odw {gdz{ ugm jrfpaufuadlfi sdumluafi mlmrjq hj~ si}{

ugm mlmrjq e}m ud ugm k}rpfu}rm al {sfkm(uahm, Au a{ ugm 5E k}rpme

{sfkm(uahm kf{m d zgfu N,N, [fb}rfa gf{ edlm dr ;E ldl(k}rpme {sfkm,

Ugm rmfia{uak kf{m rmv}arm{ ugfu ugm {sfkm om k}rpme, Uwq fku{ f{ f

smru}rofuadl f{ au a{ rm mrrme ud al V}flu}h Hmkgflak{,


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Zgml ugm{m uzd mv}fuadl{ frm s}u {aem oq {aem

HQxGfhaiudlafl 'G! 8 hj~" RMal{umal{ {urm{{ mlmrjq Uml{dr Uwq X

Mal{umal{ {urm{{ mlmrjq Uml{dr Uwq alkdrsdrfum{ jrfpaufuadl aluduga{ mv}fuadl rdh mwumrlfi {d}rkm{ dugmr ugfl lmfr ugm mfrug,

N,N,[fb}rfa gf{ }{me ugm {fhm mv}fuadl zaugd}u Mal{umal{ [urm{{

mlmrjq Uml{dr 'Uwq!

N,N,[fb}rfa{x Gfhaiudlafl 'G! 8 hj~

Hq em{krasuadl d` f sfruakim{ urfnmkudrq kdhsfrme zaug N,N, [fb}rfa{ mv}fuadl

d` f sfruakim al M}kiaemfl'ldl k}rpme! {sfkm Romidz $ dl ugm `diidzalj sfjmX


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,

UGM UGMD_Q MWUMLEME UDZF_E[ F _MIFUAPA[UAK SF_UAKIM AL

K]_PME [SFKMUAHM ][ALJ S,F,H, EA_FK[ FSS_DFKG RSFJM :X


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Strong Gravitational Lagrangian united into the Feynman Path Integral