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Solving Classical Field Equations - uni-muenchen.de
Solving Classical Field EquationsRobert C. at M unchenFeynman graphs are often thought of as tools for computations in perturbative quan-tum Field theories. However, there is nothing particularly quantum about them and, infact, Feynman rules for tree diagrams also arise when one solves Classical Field Equations ofinteracting theories ( non-linear PDEs) perturbatively. I explained this in my lectureson Introduction to Quantum Field Theory and since I am not aware of a textbook treat-ment of this material (although all this is pretty standard and known to all practitioners)I decided to write up these lecture The Klein-Gordon equation for the free fieldWe start with the Klein-Gordon equation(+m2) = arises from the actionS= ddx (+m2) .The plane wave Ansatz (t,~x) = exp(i( t ~k ~x)) is a solution provided the dispersionrelation 2 ~k2=m2holds. Upon the identification 7 Eand~k7 ~pthis is nothing but the relativisticdispersion relationE2=m2+~p2of a particle of rest massmin our units wherec= h= 1.
Solving Classical Field Equations Robert C. Helling helling@atdotde.de Ludwig-Maximilians-Universitat Mu¨nchen Feynman graphs are often thought of as tools for computations in perturbative quan-
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