dii-brain

string siddhantanusar, dii-brain, 'diriclate membrain' sathee lahan, vistarit vastooncha eka varg aahe jyavar khulya string diriclate seema attins samapt houu shakatat, jyanantar tyanna nave dilee jaatat. 
dii-brainche vargikaran samanyatah tyanchya avkashiy parimananusar kele jaate, jeey 'dii' nantar lihilelya sankhyedvare darshavile darshavile haah ekach bindu asato, asato hii eka resha asate (kadhikadhi tyala" "dii-string" "mhanatat), samantar heey eka samtal asate aanee aanee haah bosonic string siddhantat manalya manalya sarvoch-aayami jaaga bharato". tethe instantonic dii (-1)-brain dekhil aahet, jeey jaaga aanee vel yaa donhimadhye sthanbaddh aahet.
shodh.
dii-braincha shodh jiin daee, leh aanee polchinsky yanni lavala aanee swatantrapane horava yanni 1989 madhye. 1995 madhye polchinsky yanni supergravitychya kalya pii-brain dravanansah dii-brainchi olakh patavali, jyaa shodhamule kinwa superstering krantila chalana midali aanee tyamule holographic aanee emm-theary donhi dwaitata nirman jhalya.
saiddhantik parshvabhoomi.
string siddhantachya gatichya samikaranansathi aavashyak aahe qee khulya stringchya antim bindunni (antim bindunsah string) done prakarchya seema atinpaiki eka purn karane aavashyak aaheh neuman seema aut, prakashachya vegane spacetimemadhun spacetimemadhun mukt antim bindunshi sambandhit, kinwa dirichlet seema atty, jyaa string antim bindula piin karatat. stringchya pratyek nirdeshankane yapaiki eka kinwa dusari aut purn kelee pahije. mishra seema attins string dekhil astitvat asoo shakatat, jethe done antim bindu nn, dd, nd aanee dn seema atty purn karatat. jarr pii avkashiy parimane neuman seema aut purn karat asateel, tarr stringcha antim bindu pii-aayami hyperplanemadhye halanyapurta maryadit asato. heey hyperplane dii. pii.-brainche eka varnan pradan karate.
jaree shoonya jodanichya maryadet kathor asale taree, dii-brainver samapt vibhajanamule khulya taranchya varnapatat tyachya chadhautaranshi sambandhit paddhati asatat, jeey soochit karatat qee dii-brain gatishil vastoo aahet. jevha formula _ 1 dii-brain jawaljawal yogayogane asatat, tevha tyanchyamadhye pasarlelya tarancha varnapat khoop samruddha hoto. paddhatincha eka sanch jaagtik-khandavar eka gair-abelian gej siddhant tayar karato. modacha aanakhi eka sanch mhanje brainchya pratyek aadvya parimanasathi sootra _ 2 aayami matricks. jarr heey matricks pravas karat asateel tarr teey karnabaddh kele jaau shakatat aanee eigenvalues _ 1 dii-brain yaa sutrachi jaaga sthitee paribhashit karatat. adhik samanyatah, shakhanche varnan gair-vinimayatmak bhoomitidware kele jaate, jyamule myers prabhavasarkhya videshi vartanas parvanagi milate, jyamadhye dii. pii.-shakhancha sangrah dii. (pii + 2)-shakhanmadhye vistarato.
tachion ghanikaran hii yaa kshetratil eka madhyavarti sankalpana aahe. ashoke saine yanni assa yuktivad keela aahe qee aay. aay. bii. string siddhant prakarat, tachion ghanikaran (naview-schwarz 3-form fluxchya anupasthitit) anupasthitit) aanee anty anupasthitit)-brainchya stackmadhun aniyantrit dii-brain sanrachana midvanyas anumati dete. edward vitanane dakhavun dile aahe qee asha sanrachananche vargikaran spacetimechya keey-siddhantanusar kele jaeel. tachion ghanikaran ajunahi khoop qamee samajale jaate. heey tantotant string feeled siddhantachya abhavamule aahe jeey tatchionchya auph-shale utkrantiche varnan karel.
branworld cosmology.
bhautik vishvashastravar yacha parinam hoto. kaaran string siddhant soochit karato qee vishvat aaplya apekshepeksha jaast parimane aahet-26 bosonic string siddhantansathi aanee 10 superstering siddhantansathi-aaplyala atirikt parimane spasht qaa naheet yache kaaran shodhave lagel. eka shakyata ashee aahe qee drishyaman vishva heey pratyakshat teen avkashiy parimananvar vistarlele eka khoop mothe dii-brain aahe. khulya taranpasoon banavalelya bhautik vastoo dii-brainshey bandhalelya asatat aanee brainchya baherchya vishvacha shodh ghenyasathi 'vastavikatechya samkonavar' haloo shakat naheet. yaa paristhitila brain cosmology mhanatat. gurutvakarshanachi shakti khulya taranmule 'nahee' asate; gurutvakarshanachi shakti vahoon nenare gurutvakarshane hii 'bund' taranchi companshil sthitee asate. bund taranna dii-brainshey jodanyachi garaj naslyamule, gurutvakarshanache parinam brainchya orthogonal atirikt parimananvar avalambun asoo shakatat.
dii-brain scattering.
jevha done dii-brann ekmekankade jaatat tevha parasparkriya done branmadheel stringchya eka loop annulus amplityudware capture kelee jaate. done samantar shakhanchya sthir vegane ekmekanchya jawal yenyachya paristhitiche, kahee konatoon ekmekanchya sapeksh firavalelya done sthir shakhanchya samasyeshi nakash kele jaau shakate. varshik vistaramule ekatmata prapt hote jee done shakhanmadhye pasarlelya khulya taranchya khol dandyanchya utpadanashi sambandhit asate. dii-brainche shulk kitihi asale taree heey kharey aahe. sapekshata nasalelya vikhurnyachya vegat khulya taranche varnan qamee-urja prabhavi krutidvare kele jaau shakate jyamadhye done jatil scalar fields asatat jyaa formula _ 4 yaa sandnyedvare jodalya jaatat. asha prakare, feeled formula _ 5 (shakhanche pruthakkaran) badalat asatana, feeled formula _ 6 chey vastuman badalate. yamule khulya taranche utpadan hote aanee parinami done vikhuralelya fandya adaktat.
mojmap siddhant.
dii-brainchi vyavastha pranalimadhye astitvat asalelya string avasthanche prakar sankuchit karate. udaharanarth, jarr aaplyakade done samantar samantar asateel, tarr aapan sahajpane brain 1 teey brain 2 paryant kinwa tyaulat pasarlelya taranchi kalpana karoo shakato. (bahutek siddhantanmadhye, taar yaa "oriented" vastoo asatatah pratyek eka "baana" gheuun tyachya lambichya dishene paribhashit karate.) yaa paristhitit parvanagi asalelya khulya taranna nantar done shreninmadhye kinwa "kshetranmadhye" vibhagale jaateh jeey brain 1 varr ugam pavtat aanee brain 2 varr samapt hotat aanee jeey brain 2 varr ugam pavtat aanee brain 1 varr samapt hotat. pratikatmakpane, aapan mhanato qee aaplyakade [1 2] aanee [2 1] kshetra aahet. yavyatirikt, eka dori tyach brenaver suru aanee samapt houu shakate, [1 1] aanee [2 2] kshetra dete. (kansatil sankhyanna chaan-patton nirdeshank mhanatat, parantu teey kharokhar fakt shakhanchi olakh patavanare label aahet.) [1 2] kinwa [2 1] kshetramadhil eka tarchi kiman lambi asateh tee shakhanmadhil pruthakkaranapeksha lahan asoo shakat nahee. serve taranmadhye kahee taana asato, jyachya viruddha vastoo lamb karnyasathi ekhadyane khechane aavashyak asate; heey khechane taravar kaam karate, jyamule tyachi urja vadhate. kaaran string siddhant heey swabhavane sapekshavadi aahet, stringmadhye urja jodane heey einsteinchya sambandhanusar, "eae" = "emsee 2" dware vastuman jodnyaitakech aahe. mhanoon, dii-brainmadheel vibhajan kiman vastuman khulya taranvar niyantran thevate.
shivay, doricha antim bindu crainver chikatavalyane tee dori kashee haloo shakate aanee compan karoo shakate yavar parinam hoto. kaaran string siddhantatun kann sthitee vegvegalya companshil sthitee mhanoon "udbhavtat", string anubhavu shakate, dii-brainchi vyavastha siddhantat upasthit asalelya kananchya prakaranvar niyantran thevate. sarvat sope prakaran mhanje dii "pii"-brainsathi [1 1] kshetra, mhanje "pii" parimananchya konatyahi vishisht dii-brainver suru vibhajanamule aanee aanee tarancha arth. nambu-goto krutiche parinam tapastana (aanee taar mojanyasathi quantum yantrikiche niyam lagoo karane), asey aadhalate qee kananchya varnpatamadhye vidyutchumbakiy kshetrache moolbhut pariman asalelya photonshee samya asalele kann aahet. samya achook aaheh maxwellchya samikarananchya 'pii'-aayami pratirupache palan karnari vidyutchumbakiy kshetrachi 'pii'-aayami aavrutti, pratyek 'dii' pii '-brainver astitvat aahe.
yaa arthane, asey mhatale jaau shakate qee string siddhant vidyutchumbakiyatecha "andaj" lavtoh jarr aapan khulya stringsna astitvat rahanyachi parvanagi dilee tarr dii-brain haah siddhantacha eka aavashyak bhag aahe aanee serve dii-brain tyanchya aakarmanavar vidyutchumbakiy kshetra vahoon netat.
itar kann avastha tyach dii-brainver suru vibhajanamule aanee aanee taranpasoon udbhavtat. kahee photonsarkhya vastumanahin kananshi sambandhit aahet; yaa gatamadhye dekhil vastumanahin scalar kanancha sanch aahe. jarr eka dii "pii"-brain haah "dii" sthanik parimananchya antaralkalat antarbhut asel, tarr brain (tyachya kamal kshetravyatirikt) "dii-pii" vastumanahin scalarcha sanch (jyaa kananmadhye dhruvikaran nasate, jase prakash tayar naan photon) gheuun jaato. kutuhalkarak baab mhanje, brainla lumb disha aahet tevadhech vastumanahin scalar aahet; brain vyavasthechi "bhoomiti" tyavar astitvat asalelya kananchya "quantum feeled theary" shhee jawalun sambandhit aahe.kharey tarr, these massless scalars are goldstone excitations of the brane, corresponding to the different ways the symmetry of empty space can be broken. vishvat dii-brain thevane sthananmadhil samamiti todate, kaaran teey vishisht thikan paribhashit karate, aanee pratyek 'dii-pii' dishene vishisht sthanala vishisht arth niyukt karate.
maxwellchya vidyutchumbakiyatechi quantum aavrutti hii keval eka prakarcha gej siddhant aahe, eka yuu (1) gej siddhant jithe gej gut 1 kramachya ekatmak matrixpasoon banalela aahe. dii-braincha vapar uchch kramache gej siddhant tayar karnyasathi khaleel prakare keela jaau shakatoh
sadhepanasathi samantarpane mandanyat aalelya 'aine' vegalya dii 'pii'-brainchya gatacha vichar qaraa. shakhanna 1,2 asey label lavale aahe..soyisathi "aine". yaa pranalitil khulya taar anek kshetranpaiki eka bhagat astitvat aaheth kahee 'aay' yaa 'aay' yaa 'aay' yaa 'aay' yaa 'aay' yaa 'aay' yaa 'aay' yaa 'aay' yaa 'aay' yaa 'aay' yaa 'aay' yaa 'aay' yaa 'aay' yaa 'aay' yaa 'aay' yaa 'aay' yaa 'aay' yaa 'aay' yaa 'aay' yaa 'aay' yaa 'aay' yaa 'aay' yaa 'aay' yaa 'aay' yaa 'aay' yaa 'aay' yaa 'aay' yaa 'aay' yaa 'aay' yaa 'aay' yaa 'aay' yaa 'aay' yaa 'aay' yaa 'aay' yaa 'aay' yaa 'aay' aay 'yaa' aay 'aay' yaa 'aay' aay 'yaa' aay 'aay' aay 'yaa' aay 'aay' aay 'aay' aay 'aay' aay 'aay' aay 'aay' aay 'aay' aay 'aay' aay 'aay' aay 'aay' aay 'aay' aay 'aay' aay 'aay' aay 'aay' aay 'aay' aay 'aay' aay 'aay' aay 'aay' aay 'aay' aay aay' yaa 'aay' yaa 'aay' yaa 'aay' yaa 'aay' yaa 'aay' yaa 'aay' yaa 'aay' yaa 'aay' yaa 'aay' yaa 'aay' yaa 'aay' yaa 'aay' yaa 'aay' yaa 'aay' yaa 'aay' yaa 'aay' yaa 'aay' yaa 'aay' yaa 'aay' yaa 'aay' yaa 'aay' yaa 'aay' yaa 'aay' yaa 'aay' yaa 'aay' yaa 'aay' yaa 'aay' aay 'yaa' aay 'aay' yaa 'aay' aay 'yaa' aay 'aay' yaa 'aay' aay 'yaa' aay 'aay' yaa 'aay' aay 'yaa' aay 'aay' aay 'yaa' aay 'aay' aay 'yaa' aay 'aay' aay 'yaa' aay 'aay' aay 'yaa' aay 'aay' aay 'yaa' aay 'aay' aay 'yaa' aay 'aay' aay 'yaa' aay 'aay' aay 'yaa' aay 'aay' aay 'yaa' aay 'aay' aay 'yaa' aay 'aay' aay 'yaa' aay 'aay' aay 'yaa' aay 'aay' aay 'yaa suruvatichya kalat, taranche konate kshetra ekmekanshi sanvad sadhu shakatat heey vicharane fayadeshir tharate. done taranna antim bindu jodane hii eka saral paddhat aahe (kinwa, yaulat, eka tarasathi "madhyabhagi vibhajit karane" aanee done "mulgi" taar tayar karane). antim bindu dii-brainver basnyapurte maryadit asalyane, heey spasht aahe qee eka [1 2] string [2 3] stringshee parasparkriya karoo shakate, parantu [3 4] kinwa eka [4 17] stringshee nahee. varr charcha kelyapramane, yaa taranche vastuman shakhanmadhil pruthakkarnane prabhavit hoil, mhanoon sadhepanasathi, aapan kalpana karoo shakato qee shakhe ekmekanvar naan padunparyant jawalun aanee jawalun dabali jaatat. jarr aapan done paraspar aachchhadit shakhanna vegalya vastoo manale, tarr tarihi aaplyakade aadhi asalele serve kshetra aahet, parantu tee shakhanchya vibhajanamule vibhajanamule parinamanshivay aahet.
aine" concident dii-brainchya pranalisathi open-string kann spectrummadhil shoonya-vastuman sthitee parasparsanvadi quantum kshetrancha sanch dete joou agadi yuu ("aine") gej siddhant aahe. (string siddhantamadhye itar parasparsanvad asatat, parantu teey keval khoop uchch urjevar shodhanyayogya asatat.) gej siddhantancha shodh bosonic kinwa fermionic stringspasoon suru jhaala navhata; teey bhautikshastrachya vegalya kshetratun udbhavale aahet aanee tyanchya swatachya adhikarat barech upayukt jhaale aahet. jaree string siddhant haah "pratyek goshticha siddhant" nasla tarihi, dii-brain bhoomiti aanee gej siddhant yanchyatil sambandh gej parasparsanvad spasht karnyasathi eka upayukt shaikshanik sadhan pradan karato.
black hole.
dii-braincha aanakhi eka mahattvacha vapar krishna chhidranchya abhyasat jhaala aahe. 1970 chya dashakapasun, krishna chhidranmadhye entropychya samasyevar shastradnyanni vadavivad keela aahe. eka vichar prayog mhanoon, black holmadhye garam vayuche praman taknyacha vichar qaraa. chhidratil gurutvakarshanachya tanatoon vayoo baher padoo shakat naslyamule, tyachi entropy vishvatoon nahishi jhalyache disate. thermodynamicscha dusra niyam rakhanyasathi, ekhadyane asey gruheet dharale pahije qee black holala moolatah infalling gassmadhye jeey kahee entropy hote teey midale. krishna chhidranchya abhyasasathi quantum yantriki lagoo karnyacha prayatna kartana, stephen hocking shodh lavala qee chhidrane aushnik kiranotsargachya vaishishtyapurn varnpatasah urja utsarjit kelee pahije. yaa ferivalyanchya kiranotsargache vaishishtyapurn tapman asey dile jaateh
jethe "g" haah newtoncha gurutviya sthirank aahe, "m" haah krishnabinducha vastuman aahe aanee "kb" haah boltzmancha sthirank aahe.
ferivalyanchya tapmanasathi hii abhivyakti vaparoon aanee shoonya-vastuman asalelya krishnabindumadhye shoonya entropy aahe asey gruheet dharoon, "beckenstein entropy" midvinyasathi thermodynamic yuktivadancha vapar keela jaau shakatoh
beckenstein entropy hii black holchya vastuman vargala pramanbaddh asate; kaaran schwarzschild trijya vastumanala pramanbaddh asate, beckenstein entropy hii black holchya prushthbhagachya kshetrala pramanbaddh asate."kharey tarr,
jethe sootra _ 10 hii plankchi lambi aahe.
black hole entropychi sankalpana kahee manoranjak shankuvina tayar karate. eka samanya paristhitit, jevha mothya sankhyene bhinn "microstate" ekach sthool sthitichi purtata karoo shakatat tevha pranalimadhye entropy asate. udaharanarth, vayoone bharalela eka boxes dilyas, vayoo anoonchya anek vegvegalya vyavasthanmadhye samaan ekoon urja asoo shakate. tathapi, krishnagahbar hii eka vaishishtyahin vastoo asalyache manale jaat hote (johnn vhilarchya catchfragemadhye, 'krishnagahanyanna cases nasatat'). mug, 'degree auph friedam' kaay aahet jeey black hole entropyla janm deu shakatat?
taar siddhantkaranni ashee pratikruti tayar kelee aahe jyamadhye krishnavivarachi dori khoop lamb (aanee tyamule khoop mothee) asate. heey model schwarzschild black holchya apekshit entropiecy sthool karar dete, parantu achook purava adyap eka kinwa kinwa margane sapadalela nahee. mukhya adchan ashee aahe qee quantum stringmadhye asalelya degree auph friedamchi ganana karane tulanene sope aahe, jarr teey ekmekanshi sanvad sadhat nastil."heey prarambhik ushmagatikimadhye abhyasalelya aadarsh vayushi samaan aaheh jevha vayoo anoonmadhye ekmekanshi parasparsanvad nasato tevha model tayar karane sarvat sopee paristhiti asate. vayuche anoo kinwa renu aantar-kann shaktincha (vanne dair walls forcesarkhe) anubhav ghetat asha paristhitit vayuncha gativishayak siddhant vikasit karane adhik katheen aahe. tathapi, parasparsanvad nasalele jug heey eka manoranjak thikan aaheh krishnabindu samasyesathi sarvat mahattvache mhanje, gurutvakarshan haah parasparsanvad aahe aanee mhanoon jarr 'string coupling' bund kele tarr konatehi krishnabindu kadhihi udbhavu shakat nahee. mhanoon, krishnabindu entropychi ganana karnyasathi string parasparkriya astitvat asalelya vyavasthet kaam karane aavashyak aahe.
parasparsanvad naan naan taranche sope prakaran, jethe krishnagahbar astitvat asoo shakate, tyaa vyavastheparyant vistaranyasathi atisamitichi aavashyakta asate. kahee prakarananmadhye, shoonya string jodanisathi keleli entropy ganana jevha string parasparsanvad sadhatat tevha vaidh rahate. string siddhantkarasathi aavhan mhanje ashee paristhiti tayar karane jyamadhye krishnagahbar astitvat asoo shakate jeey atisamitila "todat nahee". alikadchya varshant, dii-brainmadhun krishna chhidre tayar karoon heey kele gele aahe. yaa kalpanik chhidranchya entropychi ganana kelyane apekshit beckenstein entropiecy sahmat asalele parinam midatat. durdaivane, aataparyant abhyasalelya serve prakarananmadhye uchch-aayami jaaga samavisht aahet-udaharanarth, nauu-aayami jaaget jaaget. teey aaplya swatachya vishvat vishvat schwarzschild black hole yaa parichit prakaranala thet lagoo hott naheet.
itihas.
diriclate seema atty aanee dii-brainche purn mahatva olakhanyapurvi tyancha eka dirgh 'purv-itihas' hota. bardine, baar, hanson aanee pacae yanni lihilelya 1975-76 kagadpatranchya malikemadhye, stringchya tokanvar parasparsanvadi kananchya (kwark qcd fluxes tubeshey parasparsanvad sadhatat) suruvatichya thos prastavavar charcha kelee gelee, jyamadhye stringchya antim bindunsathi gatishil seema atty hotya, jethe dirichaletchya atty sthir nasoon gatishil hotya. mishra diriclate/neuman seema atty pratham 1976 madhye warren seaglene khulya taar siddhantache gambhir pariman 26 kinwa 10 varoon 4 paryant qamee karnyache sadhan mhanoon vicharat ghetalya hotya (seaglene halpernche aprakashit karya aanee 1974 chya chodos aanee kontyachya kagadacha dekhil hawala deela aahe, parantu nantarchya kagadachya vachanavarun asey disun yete qee teey pratyakshat diriclate seema attinshi navhe tarr resheey vistar parshvabhoomishi sambandhit aahe). haah pepper jaree purvanishchit asala taree, tyachya kalat farsa ullekh keela gela navhata (seaglene 1985 madhye lihilelya 'daad super-jee string' yaa vidambanat, branworldche jawaljawal mrut varnan aahe). euclidean velesah serve nirdeshankansathi diriclate atty (jyala aata dii-instanton mhanoon olakhale jaate teey paribhashit karane) 1977 madhye michael greenne string siddhantat bindusarkhi rachana sadar karnyache sadhan mhanoon, majboot parasparsanvadacha string siddhant tayar karnyachya prayatnat sadar kele hote. harvey aanee minahan, ishibashi aanee onogi aanee 1987-89 madheel pradisi aanee sagnoti yanni abhyasalelya taranchya sankshiptatemadhye dekhil dirichlet seema atty vaparlya gelya.
1989 madhye, daee, leh, polchinsky aanee horava yanni swatantrapane shodh lavala qee tii-duality nehamichya neuman seema atinchi dirichlet seema attins adlabadal karate. yaa parinamacha arth assa aahe qee asha seema atty konatyahi khulya string siddhantachya moduli jagechya pradeshat asane aavashyak aahe. daad daee aanee itar. kagad asehi nondavato qee diriclate seema atinche sthan gatishil aahe aanee parinami vastusathi diriclate-brain (dii-brain) hii sandnya dilee jaate (haah kagad string tii-duality antargat antargat dusarya vastusathi dishabhul karnari nanee dekhil aahe). 1989 madhye leh yanni lihilelya eka peparmadhye asey disun aale qee dii-brain dynamics heey diarac-borne-infeld krutidvare niyantrit kele jaate. 1990 chya dashakachya suruvatila greenne dii-instantoncha mothya pramanavar abhyas keela aanee 1994 madhye polchinskyne shenkarne apekshit kelele naun-perterbative string prabhav tayar kelyache dakhavale. 1995 madhye polchinskyne dakhavun dile qee dii-brain heey vidyut aanee chumbakeey rammond-rammond kshetranche srot aahet jeey string dwaitatesathi aavashyak aahet, jyamule string siddhantachya naun-perterbative samajutimadhye jalad pragati hote.

