That is, we replace ∫ddk(2π)dF(\Bk)⟶∫ddk(2π)dF(\Bk)\gla(\Bk), where F(\Bk) is any function and \gla(\Bk) is the cutoff fun...That is, we replace ∫ddk(2π)dF(\Bk)⟶∫ddk(2π)dF(\Bk)\gla(\Bk), where F(\Bk) is any function and \gla(\Bk) is the cutoff function. The idea behind renormalization is that we can successively winnow degrees of freedom from a system in some exact or approximate way, and in so doing we generate a new version of the system, at a different length scale ℓ′>ℓ, and with different couplings {K′α}.
When we introduce α and e in our theory these we use the measured value of the charge of an electron – which is a solution to the full theory, not to the artificial problem with all vacuum fluctua...When we introduce α and e in our theory these we use the measured value of the charge of an electron – which is a solution to the full theory, not to the artificial problem with all vacuum fluctuations turned of. Renormalization is the mathematical procedure that express all our answers in physically sensible (measurable) quantities. A theory (such as QED) is called renormalizable if we can make all expressions finite by re-expressing them in a finite number of physical parameters.
