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9.1: The Program of Renormalization
https://phys.libretexts.org/Bookshelves/Thermodynamics_and_Statistical_Mechanics/Book%3A_Thermodynamics_and_Statistical_Mechanics_(Arovas)/09%3A_Renormalization/9.01%3A_The_Program_of_Renormalization
That is, we replace $\int\!\!{d^d\!k\over (2\pi)^d}\>F(\Bk) \longrightarrow \int\!\!{d^d\!k\over (2\pi)^d}\>F(\Bk)\,\gla(\Bk)\ ,$ where $F(\Bk)$ is any function and $\gla(\Bk)$ is the cutoff fun...That is, we replace $\int\!\!{d^d\!k\over (2\pi)^d}\>F(\Bk) \longrightarrow \int\!\!{d^d\!k\over (2\pi)^d}\>F(\Bk)\,\gla(\Bk)\ ,$ 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 $\ell'>\ell$ , and with different couplings $\{K'_\alpha\}$ .

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