Wegner-Houghton equation and derivative expansion

Details Wegner-Houghton equation and derivative expansion Wegner-Houghton equation and derivative expansion

1999-03-20

arxiv.org/abs/hep-th/9903173v1

Phys.Rev. D60 (1999) 065009

Physics

High Energy Physics

High Energy Physics - Theory

15 pages, 3 figures

Scientific paper

10.1103/PhysRevD.60.065009

We study the derivative expansion for the effective action in the framework of the Exact Renormalization Group for a single component scalar theory. By truncating the expansion to the first two terms, the potential $U_k$ and the kinetic coefficient $Z_k$, our analysis suggests that a set of coupled differential equations for these two functions can be established under certain smoothness conditions for the background field and that sharp and smooth cut-off give the same result. In addition we find that, differently from the case of the potential, a further expansion is needed to obtain the differential equation for $Z_k$, according to the relative weight between the kinetic and the potential terms. As a result, two different approximations to the $Z_k$ equation are obtained. Finally a numerical analysis of the coupled equations for $U_k$ and $Z_k$ is performed at the non-gaussian fixed point in $D<4$ dimensions to determine the anomalous dimension of the field.

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