prati-kan

kan (baayein) aur prati-kan (daayein) ke aakaar aur vidyut aavesh ka chitran. oopar se neeche ilektraun/pojeetraun,protaun/pratiproton, nyootraun/pratinyootraun.

kisi bhi kan se sambaddh pratikn bhi hota hai jiska dravyamaan abhinn hota hai lekin vidyut aavesh vipreet hota hai. udaaharan ke liye ilektraun ka prati-kan prati-ilektraun ek dhanaaveshit kan jise pojeetraun kehte hain, saamaanyat: ise rediyodharmi padaarthon ke kshaya se banaaya jaata hai.

prakruti ke niyam kanon aur pratikno ke liye lagbhag samamiteeya hote hain. udaaharan ke liye ek pratiproton aur pojeetraun se prati-haaidrojan parmaanu ka nirmaan hota hai, jiske gunadharm bhi haaidrojan parmaanu ke samaan hi hain.

prayog

pratiproton aur prati-nyootron ki khoj California vishvavidyaalaya, Berkeley mein 1955 mein emiliyo jino segre aur oven chemberlain ne ki. tab tak kan tvarak prayogon mein kai anya arddh-paramaanavik kanon ke prati-kanon ki khoj ho chuki thi. haal hi ke varshon mein prati-padaarth ke parmaanu, vishisht vidyut-chumbakeeya kshetron ki upasthiti mein prati-protaunon va pojeetraunon ke sankalan se ban chuke hain.^[1]

kotar siddhaant

diraak sameekaran ko hal karne par hamein rinaatmak oorja ki kvaantam (pramaatra) avastha praapt hoti hai. parinaam svarup ek [ilektraun apni oorja ko vikirit karte huye rinaatmak oorja avastha ko praapt ho sakta hai.

ek kalpit paayon yugm jo ki kaayon ke gaman ko prabhaavit karta hai jiske parinaamasvaroop ek udaaseen kaayon ka mishran prati-kaayon se hota hai.

yadi ek kan aur prati-kan yathochit kvaantam avastha mein hain to vo donon ek doosare ko vilupt karke koi anya kan ka nirmaan kar sakte hain. abhikriya e^- + e⁺ → γ + γ (ilektraun-pojeetraun ka do fotono mein vilopan) ek udaaharan hai. mukt aakaash mein e^- + e⁺ → γ (ilektraun-pojeetraun ka ekal foton mein vilopan) sambhav naheen hai kyonki is abhikriya mein oorja va sanveg sanrakshan donon ek saath sambhav naheen hain. yadyapi naabhik ke kulaam kshetr mein yeh sambhav hai.

kan aur pratikn ki kvaantam avasthaaon ka aavesh sanyugman (C), pairiti (Parity) (P) aur samay vyutkraman (T) sankaarako ko aaropit karke vinimay kiya ja sakta hai. yadi ${\displaystyle |p,\sigma ,n\rangle }$ ko kvaantam avastha se nirupit kiya jaaye jahaaain kan (n) ka sanveg p, spin J jiska z-disha mein ghatak σ hai, tab

${\displaystyle CPT\ |p,\sigma ,n\rangle \ =\ (-1)^{J-\sigma }\ |p,-\sigma ,n^{c}\rangle ,}$

jahaaain n^c aavesh sanyugman avastha ko nirupit karta hai, jo ki pratikn avastha hai. yadi T gatiki ki ek achhi samamiti hai to

${\displaystyle T\ |p,\sigma ,n\rangle \ \propto \ |-p,-\sigma ,n\rangle ,}$

${\displaystyle CP\ |p,\sigma ,n\rangle \ \propto \ |-p,\sigma ,n^{c}\rangle ,}$

${\displaystyle C\ |p,\sigma ,n\rangle \ \propto \ |p,\sigma ,n^{c}\rangle ,}$

jahaaain anukramaanupaati chinh darshaata hai ki yahaaain kala dakshin hasth disha mein ho sakti hai. anya shabdon mein kan aur pratikn ka

• dravyamaan m abhinn hona chaahiye.
• spin avastha J abhinn honi chaahiye.
• vidyut aavesh q aur -q vipreet hone chaahiyein.

yeh anubhaag kvaantam kshetr siddhaant ke vihit pramaatrikran ke sanket-chinh, bhaasha aur sujhaav par aadhaarit hai.

jab ham vilopan aur upojak (creation) sankaarakon ke bina ilektron ke pramaatrikran karte hain to

${\displaystyle \psi (x)=\sum _{k}u_{k}(x)a_{k}e^{-iE(k)t},\,}$

jahaaain kvaantam sankhya p aur σ ka dyotak k hai aur oorja ko E(k), vilopan sankaarak ko a_k se pradarshit kiya gaya hai. jab ham farmiyonon ki baat karte hain to sankaarak ko prati kramavinimya gunadharm ka paalan karna chaahiye tathaapi hemiltoniyn ko nimnalikhit prakaar se likha ja sakta hai

${\displaystyle H=\sum _{k}E(k)a_{k}^{\dagger }a_{k},\,}$

lekin yahaaain H pratyaashit maan ka dhanaatmak hona aavashyak naheen hai kyonki "E(k)" ka maan dhanaatmak aur rinaatmak kuchh bhi ho sakta hai aur creation tatha vilopan sankaarakon ke sanyojan ka pratyaashit maan 1 aur 0 ho sakta hai

at: hamein prati-kan prastaavit karna padta hai jiske creation aur vilopan sankaarak nimnalikhit sambandh ko santusht karte hon

${\displaystyle b_{k\prime }=a_{k}^{\dagger }\,}$ aur ${\displaystyle b_{k\prime }^{\dagger }=a_{k},\,}$

jahaaain abhinn p va viprit σ aur oorja ke viprit chinh dyotak k hai. tab ham ise kshetr ko pun: likh sakte hain

${\displaystyle \psi (x)=\sum _{k_{+}}u_{k}(x)a_{k}e^{-iE(k)t}+\sum _{k_{-}}u_{k}(x)b_{k}^{\dagger }e^{-iE(k)t},\,}$

jahaaain pratham yog dhanaatmak oorja avasthaaon va dviteeya yog rinaatmak oorja avasthaaon ke liye hai. oorja

${\displaystyle H=\sum _{k_{+}}E_{k}a_{k}^{\dagger }a_{k}+\sum _{k_{-}}|E(k)|b_{k}^{\dagger }b_{k}+E_{0},\,}$

jahaaain E₀ ek anant rinaatmak niytaank hai. nirvaat avastha shoonya kan va pratikn ${\displaystyle a_{k}|0\rangle =0}$ aur ${\displaystyle b_{k}|0\rangle =0}$ avastha hai. at: nirvaat ki oorja E₀ praapt hoti hai. chooainki sabhi oorjaaeain nirvaat ke aapekshik maapi jaati hain, H dhanaatmak nishchit hai.

faainamen–staikalabarg vivechan

• pratiknon ki gurutviya anyonya kriya
• samata, aavesh sanyugman aur vyutkram samay samamiti.
• aavesh samata ullanghan aur brahmaand ki beriyon asamamiti.
• kvaantam kshetr siddhaant aur moolabhoot kanon ki soochi
• Baryogenesis

• richrd filips faainamen (1987). "prati-kanon ke kaaran". In richrd filips faainamen aur steven vainabarg. diraak smaarak vyaakhyaanamaala 1986. Cambridge vishvavidyaalaya press. aai॰aऍsa॰abee॰aऍna॰ 0-521-34000-4.
• steven vainabarg (1995). kshetron ka pramaatra siddhaant, bhaag 1: shilaanyaas. Cambridge vishvavidyaalaya press. aai॰aऍsa॰abee॰aऍna॰ 0-521-55001-7.