  In this report we compute the boundary states (including the boundary
entropy) for the boundary sine-Gordon theory. From the boundary states, we
derive both correlation and partition functions. Through the partition
function, we show that boundary sine-Gordon maps onto a doubled boundary Ising
model. With the current-current correlators, we calculate for finite system
size the ac-conductance of tunneling quantum wires with dimensionless free
conductance 1/2 (or, alternatively interacting quantum Hall edges at filling
fraction 1/2). In the dc limit, the results of C. Kane and M. Fisher, Phys.
Rev. B46 (1992) 15233, are reproduced.
