
gaze kramaraahityam

 
saiddhaantika bhouthika saastramlo, gaze kramaraahityam anedi kramaraahityaaniki oka udaaharana-idhi quantum mechanics yokka oka lakshanam-saadhaaranamgaa oka-loop rekhaachitram-idhi quantum feeled siddhaantam yokka gaze samaruupatanu chelladu chestundi; i.ii. oka gaze siddhaantam.
anni gaze kramaraahityaalu raddu cheyabadaali. gaze samaroopatalalo kramaraahityaalu asthirataku daariteestaayi, endukante bhouthikam kaani pratikuula pramaanamtho (samaya disalo dhruveekarinchabadina photan vantivi) degrees off freedamnu raddu cheyadaaniki gaze samaruupata avasaram. nijaaniki, raddu praamaanika namoonaalo jarugutundi.
gaze kramaraahityam anae padaanni saadhaaranamgaa vector gaze kramaraahityaalaku upayogistaaru. maroka rakamaina gaze kramaraahityam gurutvakarshana kramaraahityam, endukante coordinate reparametrization (difiomorphism anie pilustaaru) anedi gurutvakarshana yokka gaze samaruupata.
kramaraahityam yokka ganana.
asamaanatalu samaana antariksha kaala kolatalalo matrame sambhavistaayi. udaaharanaku, saadhaarana 4 antariksha kaala kolatalalo kramaraahityaalu tribhuja faneman rekhaachitraala nundi utpannamavutaayi.
vector gaze kramaraahityaalu.
vector gaze kramaraahityaalalo (gaze bosan vector ayina gaze samaroopatalalo), kramaraahityam anedi kairal kramaraahityam, mariyu looplo nadustunna kairal fermiantho faneman rekhaachitram dwara sarigga oka loop sthaayilo lekkinchavacchu, loopku "n" bahya gaze bosanlatho jatacheyabadi untundi, ikkada suutram _ 1, ikkada suutram _ 2 anedi antariksha kaala parimaanam.
kairal fermians paie integrate chesina tarvaata manaku labhinche (pakshika) prabhaavavantamaina charyanu chuddam. gaze kramaraahityam unte, phalitamgaa vachhe charya gaze asthiramgaa undadu. manam suutram _ 3 dwara suuchisthee, operator anedi ε dwara anantamaina gaze parivartanaku anugunamgaa untundi, appudu frobenius sthirathvam paristhitiki idhi avasaram
edainaa kriyaatmaka suutram kosam _ 5, (pakshika) prabhaavavantamaina charya s thoo sahaa, ikkada [,] anedi abaddham brocket. suutram _ 6 anedi ε loe saralamgaa unnanduna, manam vraayavacchu.
ikkada ω (d) anedi integrated kaani kshetraala kriyaatmakamgaa d-roopam mariyu ε loe saralamgaa untundi. eee functional lokal (i.ii. ω (d) (x) anedi x vadda unna kshetraala viluvalu mariyu vaati utpannaalapai matrame aadharapadi untundi mariyu dheenini p-roopaala yokka bahya utpattigaa vyakteekarinchavachhu. space time emdi moosiveyabadithe (i.ii. sarihaddu lekunda) mariyu oriented, appudu adhi konni d + 1 dimensional oriented manifold md + 1 yokka sarihaddu. appudu manam ekapakshamgaa feeldlanu (ε thoo sahaa) md nundi md + 1 varaku nirvachinchinatlugaa avi sarihaddulato saripoladam mariyu vyakteekarana ω (d), p-roopaala bahya utpatti kaavadamtho, lopali bhaagamlo vistarinchavacchu mariyu nirvachinchavacchu, appudu
frobenius sthirathvam paristhiti ippudu avutundi
munupati sameekaranam lopali bhaagamloki kshetraala "edainaa" ekapaksha podigimpuku chellutundi kabatti,
frobenius sthirathvam paristhiti kaaranamgaa, dheeni ardham md + 1 santruptikaramgaa nirvachinchabadina d + 1-roopam ω (d + 1) (ε paie aadharapadi undadu) undhi.
ω (d + 1) nuu tarachugaa chern-simens roopam anie pilustaaru.
marosari, ω (d + 1) nuu bahya utpattigaa vyakteekarinchavachani mariyu daanini d + 2 dimensional oriented manifold loe d + 1-roopamloki vistarinchavacchani manam bhaavisthe, manam nirvachinchavacchu.
d + 2 kolatalalo. ω (d + 2) anedi gaze asthiramgaa untundih
d mariyu δε prayaanamgaa.

