378 CHAPTER24. THEFEYNMANPATHINTEGRAL
Whythen,havewespentthewholeyearfollowingtheSchrodingerequationap-
proach? Why notbeginwithpath-integral, andsolvebound-stateand scattering
problems bythat method? Infact, suchan approachtoteachingnon-relativistic
quantummechanicscanbeandhasbeenfollowed,byFeynmanhimself.Theresults
areenshrinedinatextbookbyFeynmanandHibbs. However,nootherelementary
textbook,andnotmanyinstructors,havefollowedFeynman’sexample. Thereason
issimplythat,innon-relativisticquantummechanics,thepath-integralisarather
cumbersomeprocedureforsolvingproblems,ascomparedtotheSchrodingerequa-
tion.
Inrelativisticquantumfieldtheory, however,thesituationisdifferent: forvery
manyproblemsitisthepath-integraltechnique whichiseasier touse, andbetter
adaptedthanoperatormethodstothethornytechnicalitiesthatareencountered.As
abonus,thepath-integralformulationisnaturallysuitedtovariousnon-perturbative
approximationmethods,suchastheMonteCarloprocedure,incaseswherepertur-
bationtheorycannotbeapplied.Finally,thereareinterestinganddeepconnections
betweenquantumfield theory, basedon theFeynampath integral, andstatistical
mechanics,basedontheanalysisofapartitionfunction. Butthisisalongstory,to
betaughtinanother,moreadvanced,course.