Renormalization group methods and the 2PI effective action

We consider a symmetric scalar theory with quartic coupling in 4-dimensions and compare the standard 2PI calculation with a modified version which uses a functional renormalization group method. The set of integral differential equations that are obtained from the exact renormalization group method truncate naturally, without the introduction of additional approximations. The results of the two methods agree well, which shows that the exact renormalization group can be used at the level of the 2PI effective action to obtain finite results without the use of counter-terms. The method therefore offers a promising starting point to study the renormalization of higher order $n$PI theories.

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