ity , ▁namely ▁the ▁Hamiltonian ▁constraint ▁of ▁L Q G ; ▁this ▁choice ▁made ▁its ▁second , ▁form id able , ▁term ▁van ish ▁and ▁the ▁remaining ▁term ▁became ▁polynomial ▁in ▁his ▁new ▁variables . ▁This ▁raised ▁new ▁hopes ▁for ▁the ▁canonical ▁quantum ▁gravity ▁programme . ▁However ▁it ▁did ▁present ▁certain ▁difficulties . ▁Although ▁Ash te kar ▁variables ▁had ▁the ▁virtue ▁of ▁simpl ifying ▁the ▁Hamiltonian , ▁it ▁has ▁the ▁problem ▁that ▁the ▁variables ▁become ▁complex . ▁When ▁one ▁quant izes ▁the ▁theory ▁it ▁is ▁a ▁difficult ▁task ▁to ▁ensure ▁that ▁one ▁re co vers ▁real ▁general ▁relativ ity ▁as ▁opposed ▁to ▁complex ▁general ▁relativ ity . ▁Also ▁the ▁Hamiltonian ▁constraint ▁Ash te kar ▁worked ▁with ▁was ▁the ▁dens it ized ▁version ▁instead ▁of ▁the ▁original ▁Hamiltonian , ▁that ▁is , ▁he ▁worked ▁with ▁. ▁There ▁were ▁serious ▁difficulties ▁in ▁prom oting ▁this ▁quantity ▁to ▁a ▁quantum ▁operator . ▁It ▁was ▁Thomas ▁Th iemann ▁who ▁was ▁able ▁to ▁use ▁the ▁general ization ▁of ▁Ash te kar ' s ▁formal ism ▁to ▁real ▁connections ▁( ▁takes ▁real ▁values ) ▁and ▁in ▁particular ▁de vised ▁a ▁way ▁of ▁simpl ifying ▁the ▁original ▁Hamiltonian , ▁together ▁with ▁the ▁second ▁term , ▁in ▁ 1 9 9 6 . ▁He ▁was ▁also ▁able ▁to ▁promote ▁this ▁Hamiltonian ▁constraint ▁to ▁a ▁well ▁defined ▁quantum ▁operator ▁within ▁the ▁loop ▁representation . ▁For ▁an ▁account ▁of ▁these ▁develop ments ▁see ▁John ▁B ae z ' s ▁home page ▁entry , ▁The ▁Hamiltonian ▁Con stra int ▁in ▁the ▁Loop ▁Represent ation