  The isospectral renormalization group is a powerful method to analyze the
spectrum of operators in quantum field theory. It was introduced in 1995 [see
\cite{BachFrohlichSigal1995}, \cite{BachFrohlichSigal1998}] and since then it
has been used to prove several results for non-relativistic quantum
electrodynamics. After the introduction of the method there have been many
works in which extensions, simplifications or clarifications are presented (see
\cite{BachChenFrohlichSigal2003}, \cite{GriesemerHasler2008},
\cite{FrohlichGriesemerSigal2009}). In this paper we present a new approach in
which we construct a flow of operators parametrized by a continuous variable in
the positive real axis. While this is in contrast to the discrete iteration
used before, this is more in spirit of the original formulation of the
renormalization group introduced in theoretical physics in 1974
\cite{KogutWilson1974}. The renormalization flow that we construct can be
expressed in a simple way: it can be viewed as a single application of the
Feshbach-Schur map with a clever selection of the spectral parameter. Another
advantage of the method is that there exists a flow function for which the
renormalization group that we present is the orbit under this flow of an
initial Hamiltonian. This opens the possibility to study the problem using
different techniques coming from the theory of evolution equations.
