Electromagnetism and renormaliztion

[eljose79]

i always have asked myself this question ..Feynmann and others got the nobel prize for quantizaying the electromagnetism..i have read about it and it seems it was a difficult task..but why not try this way .take the lagrangian of electromagnetism and take the hamiltonian to be H=E+B now we now E=-dA/dt and B=rotA so we could quantizy the hamiltonian and get the wave functional F(A) with
HF(A)=EF(A) what is easier...then why use renormaliztion and all that?..in electromagnetism can the Hamiltonian description presented above describe quantum electormagnetism?..then why qed?..

 

[Anton A. Ermolenko]

Originally posted by eljose79
i always have asked myself this question ..Feynmann and others got the nobel prize for quantizaying the electromagnetism..i have read about it and it seems it was a difficult task..but why not try this way .take the lagrangian of electromagnetism and take the hamiltonian to be H=E+B now we now E=-dA/dt and B=rotA so we could quantizy the hamiltonian and get the wave functional F(A) with
HF(A)=EF(A) what is easier...then why use renormaliztion and all that?..in electromagnetism can the Hamiltonian description presented above describe quantum electormagnetism?..then why qed?..

Hi eljose79
Because "this way" explains nothing. Just try to calculate the anomalous magnetic moment of electron by "this way"... of course you can't...

 

[selfAdjoint]

In fact the Lagrangean for QED consists of the sum of the Dirac Lagrangean, the Maxwell Lagrangean, and an interaction term. The quantization of this was highly nontrivial, and you can read about the struggles of the people involved in Schweber's fine history "QED and the Men who Made it".