1 9 1 9 ▁and ▁Nor bert ▁Wiener ▁in ▁a ▁series ▁of ▁studies ▁cul min ating ▁in ▁his ▁articles ▁of ▁ 1 9 2 1 ▁on ▁Brown ian ▁motion . ▁ ▁They ▁developed ▁a ▁rig orous ▁method ▁( now ▁known ▁as ▁the ▁Wiener ▁measure ) ▁for ▁assigning ▁a ▁probability ▁to ▁a ▁particle ' s ▁random ▁path . ▁ ▁Richard ▁Fe yn man ▁developed ▁another ▁functional ▁integral , ▁the ▁path ▁integral , ▁useful ▁for ▁computing ▁the ▁quantum ▁properties ▁of ▁systems . ▁ ▁In ▁Fe yn man ' s ▁path ▁integral , ▁the ▁classical ▁notion ▁of ▁a ▁unique ▁traject ory ▁for ▁a ▁particle ▁is ▁replaced ▁by ▁an ▁infinite ▁sum ▁of ▁classical ▁paths , ▁each ▁weight ed ▁differently ▁according ▁to ▁its ▁classical ▁properties . ▁ ▁Function al ▁integration ▁is ▁central ▁to ▁quant ization ▁techniques ▁in ▁theoretical ▁physics . ▁ ▁The ▁algebraic ▁properties ▁of ▁functional ▁integr als ▁are ▁used ▁to ▁develop ▁series ▁used ▁to ▁calculate ▁properties ▁in ▁quantum ▁elect rod ynam ics ▁and ▁the ▁standard ▁model ▁of ▁particle ▁physics . ▁ ▁Function al ▁Integr ation ▁ ▁Where as ▁standard ▁Riemann ▁integration ▁sums ▁a ▁function ▁f ( x ) ▁over ▁a ▁continuous ▁range ▁of ▁values ▁of ▁x , ▁functional ▁integration ▁sums ▁a ▁functional ▁G [ f ], ▁which ▁can ▁be ▁thought ▁of ▁as ▁a ▁" function ▁of ▁a ▁function " ▁over ▁a ▁continuous ▁range ▁( or ▁space ) ▁of ▁functions ▁f . ▁Most ▁functional ▁integr als ▁cannot ▁be ▁evaluated ▁exactly ▁but ▁must ▁be ▁evaluated ▁using ▁perturb ation ▁methods . ▁The ▁formal ▁definition ▁of ▁a ▁functional ▁integral ▁is ▁