
moyal bracket

bhauthikashaasthrathil, moyal bracket ennathu ghattam-bahirakasha nakshatra uthppannathinte uchithamaaya saadhaaranavalkkaricha antisemetriseshanaanu.
1940ll jose enriq moyal aanu moyal bracket vikasippicheduthathenki pooll dirakkumaayulla neenda tharkkathinu sesham 1949ll maathramaan moyal thante kruthi prasidheekarikkaan kazhinjathu. ithinidayil 1946ll hip gronwold eee ashayam swathanthramaayi avatharippichu.
avalokanam.
eee nireekshanavasthukkale ghatta idathile pravarthanangalaayi vivarikkumbol kwaandam mekkaaniksinte ghattam space roopeekaranathil nireekshanavasthukkalude commutatorine vivarikkunnathinulla oru maargamaan moyal bracket. kwaandam observatable upayogichu ghatta idathile functionukal thirichariyunnathinulla skeemukale ithu aasrayikkunnu, eee skeemukalil ettavum prashasthamaayath wigner-weyl parivarthanamaanu. ithu highsenberghinte chalanatthinte kwaandam samavaakyathin thulyamaaya roopeekaranamaaya moyalinte chalanathmaka samavaakyathin adivarayidunnu, athuvazhi haamilttaninte samavaakyangalude kwaandam saamaanyavalkkaranam nalkunnu.
ganithashaasthraparamaayi, ithu phase-space poyson braakkattinte (adisthaanaparamaayi athinte oru vipuleekaranam) oru roopabhedamaanu, roopabhedam paaraameettar kuranja plank sthiraankamaanu. athinaal, athinte group sankochathinu beejaganitam enna pooyisan bracket labhikkunnu.
aupachaarika thulyatha vare, moyal bracket ennathu poyson braakkattinte "advitheeyamaaya oru-paaraameettar lye-algibraic roopabhedam" aanu. kammyoottettarukalude beejaganithathodulla athinte beejaganita isomorphism gronwold-vaan hove sidhaanthathinte negatteevu phalathe marikadakkunnu, ithu poyson brackettinulla atharam isomorphisathe thadayunnu, 1926 leeii doctoral theesisil dirac parokshamaayi unnayicha oru chodyam, kwaandaiseshanulla "classical analogy reethi".
udaaharanathinu, oru dvimaana paranna ghatta idathilum weyl-mapp correspondencinum moyal bracket ingane vaayikkunnu
ghatta idathile nakshatra-uthppanna oopparettar evideyaanu (cf. moyal uthppannam), avaa deferentiable phase-space functionukalaanu, avayude poyson brackettaanu.
kooduthal vyakthamaayi paranjaal, pravarthanaparamaaya calculus bhashayil ithu thulyamaanu.
bhagika derivetteevukalkk mukalilulla idathu, valath ambukal idathu, valath bhagika derivetteevukale soochippikkunnu. chilappol moyal brackettine "saine bracket" ennu vilikkunnu.
jorjju baker avatharippicha oru janapriya (forrier) avibhaajya praathinidhyam
ghattam muthal hilbert vareyulla oro correspondence mappum oru savisheshamaaya "moyal" bracket (weyl maappinaayi ivide chithreekarichirikkunnathu pole) ulkkollunnu. atharam moyal brackettukalellaam oru chittayaya sidhaanthathinu anusrithamaayi avaa thammil "aupachaarikamaayi thulyamaanu".
moyal bracket namakaranam cheytha ananthamaaya alavukoline vyakthamaakkunnu 
beejaganitam-ithu athinte vaadangalil antisemetric aanu, koodaathe jacoby identitye thripthippeduthunnu.
anubandha amoorthamaaya nuna beejaganitam manassilaakkunnath, angane 
2-torres ghatta idathil, aanukaalikamaayi 
adisthaana functionukalkkaayi, kordinettukalum, oro inn, intijar mooad soochikakalum, eee lye aljibra vaayikkunnu
ithu poornnasamkhyaykku "suu" ("enn") aayi kurayunnu.
"suu" ("" n "") pinneedu 1/"" n "" enna roopabhedam parameterinoppam "" suu "" (φ) enna roopabhedamaayi uyarnnuvarunnu ".
randaam klaas parimithikalulla kwaandam sistangalkkaayulla moyal braakkattinte saamaanyavalkkaranathil ghatta idathile functionukalude thulyatha klaasukalile oru pravartthanam ulppedunnu, ithu diarac braakkattinte kwaandam roopabhedamaayi kanakkakkaam.
saine bracket kosain bracket.
charcha cheytha saine brackettinu aduthaayi, gronwold baker vishadeekaricha kosain bracket avatharippichu,
ivide, veendum, ghatta idathile nakshatra-uthppanna oopparettaraanu, avaa deferentiable ghatta-sthala pravarthanangalaanu, ithu saadhaarana ulppannamaanu.
saine, kosain brackettukal yathaakramam nakshatra uthppannathe antisemetriging, simetrijing ennivayude falamaanu. athinaal, saine bracket commutettarinte wigner mapp aayathinal, staanderd kwaandam mechanicsile aantikamyoottettint wigner imej aanu kosain bracket. athupole, moyal bracket uyarnna oordarukal vareyulla poyson brackettinu thulyamayathinaal, kosain bracket uyarnna oordarukal vareyulla saadhaarana uthppannathin thulyamaanu. classical paridhiyil, moyal bracket leovil samavaakyathilekku (poyson braakkattinte adisthaanathil roopappeduthiya) kuraykkaan sahayikkunnu, kaaranam kosain bracket classical haamilttan-jacoby samavaakyathilekku nayikkunnu.
saine, kosain bracket enniva kwaandam mekkaaniksinte poornnamaayum beejaganita vivaranathinte samavakyangalumaayi bandhappettirikkunnu.