Multichannel impurity scattering in a Tomonaga-Luttinger liquid

Using an elementary method, we demonstrate that (1) the duality of the correlation exponents near impurity site x=0 between ultraviolet and infrared fixed points is also valid for channel number larger than one; (2) the infrared fixed points delta(c)(i)=+/-pi/2 do not correspond to two real half-infinity Tomonaga-Luttinger liquids even if the conductance is zero; (3) the electron's density of state at x=0 is enhanced compared with its neighbor ones; (4) as channel number is larger than (or equal to) two, the Fermi-edge singularity induced by backward scattering will be swept off by even small repulsive interaction of the electrons. [S0163-1829(98)07519-5].