Quantum Field Theory - In a Nutshell

Ultraviolet Divergence

     ". . .in quantum field theory infinity is equal to zero and that under the rug in a field theorist's office had ben swept many infinities." Zee

    "When calculating terms with couplings, we must consider all possible points where couplings can ocur, right down to the cases where two coupling points are on top of each other--with zero distance between them. When we try to calculate all the way down to zero distance, the equation blows up in our face and gives us meaningless answers--things like infinity. People were getting infinity for every problem they tried to calculate!" Feynman

A. Zee's take on Renormalization
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Quantum Field Theory without Divergences or Renormalization, I

Quantum field theory--Fifty years of the renormalization group

The Dirac Equation