▁Call an - Sym anz ik ▁equation ▁rel ates ▁these ▁sh ifts : ▁ ▁After ▁the ▁following ▁definitions ▁ ▁the ▁Call an - Sym anz ik ▁equation ▁can ▁be ▁put ▁in ▁the ▁conventional ▁form : ▁▁ ▁being ▁the ▁beta ▁function . ▁ ▁In ▁quantum ▁elect rod ynam ics ▁this ▁equation ▁takes ▁the ▁form ▁ ▁where ▁n ▁and ▁m ▁are ▁the ▁numbers ▁of ▁electron ▁and ▁phot on ▁fields , ▁respectively , ▁for ▁which ▁the ▁correlation ▁function ▁ ▁is ▁defined . ▁The ▁ren ormal ised ▁coupling ▁constant ▁is ▁now ▁the ▁ren ormal ised ▁elementary ▁charge ▁e . ▁The ▁electron ▁field ▁and ▁the ▁phot on ▁field ▁res c ale ▁differently ▁under ▁ren ormal isation , ▁and ▁thus ▁lead ▁to ▁two ▁separate ▁functions , ▁ ▁and ▁, ▁respectively . ▁ ▁The ▁Call an - Sym anz ik ▁equation ▁was ▁discovered ▁independently ▁by ▁Curt is ▁Call an ▁and ▁Kurt ▁Sym anz ik ▁in ▁ 1 9 7 0 . ▁Later ▁it ▁was ▁used ▁to ▁understand ▁asympt otic ▁freedom . ▁ ▁This ▁equation ▁ar ises ▁in ▁the ▁framework ▁of ▁ren ormal ization ▁group . ▁It ▁is ▁possible ▁to ▁treat ▁the ▁equation ▁using ▁perturb ation ▁theory . ▁ ▁See ▁also ▁Ex act ▁ren ormal ization ▁group ▁equation ▁B eta ▁function ▁ ▁Notes ▁ ▁References ▁ ▁Jean ▁Z inn - Just in , ▁Quant um ▁Field ▁Theory ▁and ▁Crit ical ▁Ph en omena ▁, ▁Oxford ▁University ▁Press , ▁ 2 0 0 3 , ▁▁ ▁John ▁Clement s ▁Collins , ▁Ren ormal ization , ▁Cambridge ▁University ▁Press , ▁ 1 9