How Does Renormalization Address Divergences in Integrals?

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SUMMARY

Renormalization effectively addresses divergences in integrals by applying functional differentiation with respect to the exponential term e^{-ax}. In the discussed scenario, the integral takes the form ∫_{R}dx C(x)w(x)e^{-ax}, where 'a' is a divergent quantity represented as a=ln(ε). The process reveals that the divergent term vanishes, demonstrating the utility of renormalization in managing infinite series within quantum field theory.

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eljose
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for a divergent series i can write an expression in the form:

\int_{R}dxC(x)w(x)e^{-ax}

where a is a divegent quantity in the form a=ln\epsilon

the qeustion is how i would apply renormalization?..in fact if we apply functional differentiation respect to e^{-ax} we get

C(x)w(x) the divergent term magically disappears
 
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