We calculate the linear response conductance of electrons in a Luttinger
liquid with arbitrary interaction g_2, and subject to a potential barrier of
arbitrary strength, as a function of temperature. We first map the Hamiltonian
in the basis of scattering states into an effective low energy Hamiltonian in
current algebra form. Analyzing the perturbation theory in the fermionic
representation the diagrams contributing to the renormalization group (RG)
\beta-function are identified. A universal part of the \beta-function is given
by a ladder series and summed to all orders in g_2. First non-universal
corrections beyond the ladder series are discussed. The RG-equation for the
temperature dependent conductance is solved analytically. Our result agrees
with known limiting cases.Comment: 6 pages, 5 figure