sthool-naview model

sthool-nivyu (jee. aine.) model heey diarac fermionche eka quantum kshetra siddhant model aahe jeey 1 avkashiy aanee 1 vel parimanat chaar-fermian parasparsanvadvare parasparkriya karate. 1974 madhye david gross aanee andre naview yanni quantum chromodynamics (qcd) sathee khelani model mhanoon, majboot parasparsanvadacha siddhant mhanoon yachee olakh karoon dilee. tyat kyu. see. dii. chee anek vaishishtye samayik kelee jaatatah jee. aine. siddhant asymptotically mukt aahe, tyamule majboot jodanimadhye parasparsanvadachi takad kamkuvat hote aanee parasparsanvad jodaniche sambandhit sootra _ 1 karya nakaratmak asate, siddhantamadhye sootra _ 2 kieral samamiti todanyasah gatishil vastuman nirmiti yantrana asate aanee mothya sankhyene swad (sootra _ 3) maryadet, jee. aine. siddhant kyu. see. dii. madhye tii 'hooftchya mothya sootra _ 4 maryada mhanoon vagato.
tyat aine diarac fermians sootra _ 5 asate. lagrangian ghanata aahe
einstein berries sanketan vaparale jaate, sootra _ 7 haah done ghatak spinor object aahe aanee sootra _ 8 haah jodani sthirank aahe. jarr vastuman sootra _ 9 shoonya naslyas, model shastriyadrushtya mothe aahe, anyatha tyala kieral samamiti milate.
yaa pratimanat yu (aine) jaagtik antargat samamiti aahe. jarr konee n = 1 ghetala (joou keval eka chaturthansh parasparsanvadas parvanagi deto) aanee pariman vishleshanatmakapane chaloo thevanyacha prayatna keela nahee, tarr model mothya tring modelmadhye qamee hote (jeey purnapane samakalit aahe).
hii 4-aayami nambu-jona-lecinio modelchi (aine. jeey. ell.) 2-aayami aavrutti aahe, jee 14 varshanpurvi bii. see. see. chya atichalakta siddhantavar aadharit gatishil kieral samamiti todanyache (parantu kwark bandee nahee) model mhanoon sadar karnyat aalee hotee. 2-aayami aavrutticha fayda assa aahe qee 4-fermi parasparkriya hii punha samanya karnyayogya aahe, jee konatyahi mothya parimananmadhye nahee.
siddhantachi vaishishtye.
ekoon aanee naview yanni yaa modelcha abhyas mothya sootra _ 10 maryadet keela, 1/n vistaramadhye sambandhit mapdandancha vistar keela. heey aanee sambandhit model heey lakshanrahitpane mukt aahet heey dakhavun dilyanantar, tyanna aadhalale qee, up-agraganya kramane, lahan fermian vastumanansathi bifermian condensate sootra _ 11 nirvat apeksha moolya (vhee. vhee. vhee.) prapt karate aanee parinami moolbhut fermian prachand hotat. tyanna asey aadhalale aahe qee jodani sthirank g madhye vastuman vishleshanatmak nahee. nirvat apeksha moolya utsfurtapane siddhantachi kieral samamiti todate.
adhik tantotantpane, dvirekheey ghanarupasathi nirvat apeksha moolya nasalelya nirvatabaddal vistar kartana tyanna eka tachion sapadala. heey karnyasathi teey dvi-vibhajak kshetrachya prasarkansathi punar-samanyikaran gut samikarane sodavtat, yaa vastusthiticha vapar karoon qee jodani sthirankache ekmev punar-samanyikaran sammishra kshetrachya tarang karya punar-samanyikaranatun yete. tyanantar tyanni ganana kelee, 1/n vistaramadhye agraganya kramane parantu jodani sthirankachya serve kramansathi, mageel varshi iris international summer school auph physicsmadhye sidney kolemanne sadar kelelya prabhavi krutee tantrancha vapar karoon ghanarupavaril sambhavya urjeche avalambitva. tyanna aadhalale qee hii kshamata ghanikaranchya shunyetar mulyanusar qamee kelee jaate, jeey heey ghanikaranche kharey moolya asalyache darshavate. naveen nirvatabaddalachya siddhantacha vistar kartana, tachion aata astitvat nasalyache aadhalun aale aanee kharey tarr, bii. see. see. chya ativahakta siddhantapramane, tethe vastuman antar aahe.
tyanantar tyanni quantum kshetra siddhantanmadhye gatishil vastuman nirmitibaddal anek samanya yuktivad kele. udaharanarth, tyanni dakhavun dile qee infrared-sthir asalelya siddhantanmadhye serve vastuman gatishilpane tayar kele jaau shakat naheet, yacha vapar assa yuktivad karnyasathi keela qee, kiman 1/n madheel agrakramasathi, 4-aayami sootra _ 12 siddhant astitvat nahee. tyanni assa yuktivadahi keela qee asymptotically free thearysmadhye gatishilpane nirman jhalele vastuman kadhihi vishleshanatmakdrushtya coupling sthirankanvar avalambun nasate.
samanyikaran.
sthool aanee naview yanni anek samanyikaranancha vichar keela. pratham, tyanni eka atirikt chaturthansh parasparsanvadasaha lagrangian manale
mool pratikrutiche swatantra kieral samamiti sootra _ 14 heey satat yu (1)-moolya asalelya kieral samamiti sootra _ 15 madhye vadhavanyasathi nivadle gele aahe. kieral samamiti todane purvipramanech hote, jeey tyach vvmule hote. tathapi, utsfurtapane tutaleli samamiti aata satat asalyane, varnapatat eka vastumanahin sonyacha dagad boson disato. jaree yamule 1/n vistaramadhye agraganya kramane konatihi samasya udbhavat nasali, taree dvimiteey quantum kshetra siddhantanmadhil vastumanahin kann apariharyapane infrared vichalanankade netat aanee tyamule siddhant astitvat nasalyache disate.
tyanantar yaa samasyevar upay upay sudharit siddhantachya aanakhi done badalancha vichar karnyat aala. eka badalamadhye eka parimananchi sankhya vadhavato. parinami, vastumanahin kshetramule vichalan hott nahee. nahee badalamadhye kieral samamitiche mojmap kele jaate. parinami, photon prachand hott asalyane aanee tyamule konatehi vichalan hott nasalyane, goalstone boson heey uchch yantradvare khalle jaate.

