
noonn commutative kwaandam feeld sidhaantham

ganithashaasthra bhauthikashaasthrathil, noonn commutative kwaandam feeld sidhaantham (allengil noonn commutative space timinekkurichulla kwaandam feeld sidhaantham) ennathu noonn commutative jyaamithiyudeyum soochika sidhaanthathinteyum valarchayaan, ithu noonn commutative jyaamithiyudeyum soochika sidhaanthathinteyum space timilekku noonn commutative ganithashaasthrathinte prayogamaanu. atharam sidhaanthangalude saadhaaranayaayi padicha oru pathippin "canonical" commutation bandhamunda
athaayath (eathenkilum nischitha achuthandukal upayogichu), onniladhikam achuthandukalumaayi bandhappett oru kanikayude sthaanam krithyamaayi alakkunnathu asaadyamaanu. vaasthavathil, ithu heisenberg anishchithathva thathwathinu samanamaaya kordinettukalkkulla anishchithathva bandhatthilekku nayikkunnu.
noonn commutative scalinaayi vividha thaazhnna paridhikal avakaashappettittund, (i.iii. sthaanangal ethra krithyamaayi alakkaan kazhiyum) ennaal atharam oru sidhaanthathinu anukoolamaayi nilavil pareekshanathmaka thelivukaloo avaa thallikkalayaanulla adisthaanangalo illa.
noonn commutative feeld sidhaanthangalude puthiya savisheshathakalilonnaanu uyarnna oorjjathilulla bhauthikashaasthram kuranja oorjjathil bhauthikashaasthrathe badhikkunna yuvi/ir mixing prathibhasam, ithu kordinettukal sanjarikkunna kwaandam feeld sidhaanthangalil sambhavikkunnilla.
noonn kammyoottattivittiyu munganana kaaranam laurents inveriyansinte lamghanam mattu savisheshathakalil ulppedunnu. ennirunnaalum sidhaanthathinte valanja poincare invarians enna ardhathil aapekshikathayude invarians nilanirthaan kazhiyum. commutative sidhaanthangalil ninnu kaaryakaaranaavastha parishkarichirikkunnu.
charithravum prachodanavum.
punarroopakalppana prakriya vikasippikkukayum amgeekaaram nedukayum cheiyunnathinu munbu feeld sidhaanthangalil prathyakshappedunna ananthamaaya alavukal neekkam cheiyunnathinulla saadhyamaaya maargamaayi kordinettukalilekku noonn commutattivitti vyaapippikkaan aadyamaayi nirddeshichathu heisenbergaanu. eee vishayathekkurichulla aadya prabandham 1947ll hartland snider prasidheekarichu. punarroopakalppana reethiyude vijayam kurachukaalathekku vishayathin kaaryamaaya shradha nalkaathathinu kaaranamaayi. 1980kalil ganithashaasthranjar, prathyekichu alan koons, noonn commutative jyamiti vikasippichu. mattu karyangalkkoppam, eee kruthi deferential ghadana enna ashayathe oru noonn commutative krameekaranatthilekku saamaanyavalkkarichu. ithu noonn commutative space-timesinekkurichulla oru oopparettar beejaganita vivaranathilekku nayichu, ithu classicalaayi positteev aayi nirvachikkapetta metrik tensorumaayi oru maanifoldumaayi poruthappedunnu enna prashnathode, eee sameepanathil (noonn commutative) kaaryakaaranathekkurichu oru vivaranavumilla. ennirunnaalum, ithu oru noonn commutative torresinekkurichulla yang-mill sidhaanthathinte vikasanathinum kaaranamaayi.
nathan seaburghinteyum edward vittanteyum oru prabandham kaaranam kanika bhauthikashaasthra samoohathinu noonn commutative sameepanathil thaalpparyamundaayi. brainile sthiramaaya kaanthikakshethrathinu thulyamaaya oru sthiramaaya neview-schwarz bii-feeldinte saannidhyathil thuranna stringukalude end pooyintukalude coordinate functionukal oru dii-brainilekk parimithappedutthiyittunne avar string sidhaanthathinte pashchaathalatthil vaadichu. noonn commutative space timinekkurichulla oru kwaandam feeld sidhaanthathe ooppan stringukalude sidhaanthathinte kuranja oorjja paridhiyayi vyaakhyaanikkaam ennathaanu ithinte ardham.
sergio doplisher, closs fredenhagen, joonn roberts ennivarude rund prabandhangal 
mattonn dii. vii. aluwalia,
space-time enna aashayavinimayathinte saadhyathayulla noonn commutattivittikk mattoru prachodanam nalkuka. 
vaadangal iprakaaramaanu pothuvaaya aapekshikatha anusarichu, oorjja saandrata vendathra valuthayi valarumbol oru thamogarthatthinu roopam nalkunnu. maruvashathu, heisenberg anishchithathva thathwam anusarichu, oru space-time seppareshan alakkunnathu seppareshante vyaapthikk vipareeta anupaathathil momentatthil anishchithathvathinu kaaranamaakunnu. athinaal, aakkam anishchithathvavumaayi poruthappedunna oorjjam sthaanathile anishchithathvavumaayi poruthappedunna oru pradeshathinullile sisttathil praadeshikavalkkarikkuppadu. verthirikkal mathiyaya cheruthaanenkil, sisttathinte schwarz child aaram athukayum oru thamogartthamundaakkukayum cheiyunnu, ithu sisttathil ninnu eathenkilum vivarangal rakshappedunnathil ninnu thadayunnu. athinaal neelam alakkunnathinu oru thaazhnna paridhiyund. guruthwaakarshana thakarcha thadayunnathinulla mathiyaya vyavastha kordinettukalude anishchithathva bandhamaayi prakadippikkaam. eee bandham kordinettukalkkulla oru commutation bandhatthil ninnu uruthirinjekkaam.
mattu sameepanagalil ninnu vyathyasthamayi, prathyekichu koons aashayangale ashrayikkunnavar, ivide noonn commutative space time sariyaaya space time aanennu oonnipparayendathundu, athaayath.iii. ithu oru naalumitheeya suedo-remanian ashayathe palamadangu vikasippikkunnu. maruvashathu, konsinte noonn commutative jyamithiyil ninnu vyathyasthamayi, nirddishta model aadyam muthal aashrayichirikkunna kordinettukalaayi maarunnu.
doplisher fredenhagen robertsinte paper noonn commutattivitti oof kordinettukal speshyal kordinettukale mathramalla, naalu space time kordinettukaleyum badhikkunnu.

