4 research outputs found
The local potential approximation in the background field formalism
Working within the familiar local potential approximation, and concentrating
on the example of a single scalar field in three dimensions, we show that the
commonly used approximation method of identifying the total and background
fields, leads to pathologies in the resulting fixed point structure and the
associated spaces of eigenoperators. We then show how a consistent treatment of
the background field through the corresponding modified shift Ward identity,
can cure these pathologies, restoring universality of physical quantities with
respect to the choice of dependence on the background field, even within the
local potential approximation. Along the way we point out similarities to what
has been previously found in the f(R) approximation in asymptotic safety for
gravity.Comment: 40 pages, version accepted by JHE