D. Schmeltzer et Ar. Bishop, BOSONIZATION IN 2 DIMENSIONS - A SPACE-TIME TUNNELING APPROACH, Physical review. B, Condensed matter, 50(17), 1994, pp. 12733-12743
Using the space-time curve representation, a bosonization scheme is co
nstructed which includes density excitations around each point on the
Fermi surface (FS) and space-time tunneling of charges which belong to
different FS points. The space-time tunneling reproduces the two-dime
nsional Jordan-Wigner transformation. In two dimensions, since the tun
neling involves two electrons, the total Jordan-Wigner phase maps boso
n into boson. Therefore, the tunneling corresponds to instantons in 2e
bosonic systems. Using this formalism, a spinless fermion model with
short-range repulsive interactions is investigated. We find two compon
ents: sound-wave excitations in the normal direction of the FS reprodu
ce the Fermi liquid (FL); the second component corresponds to the coop
eron channel, violates charge conservation, and gives rise to two-part
icle coherent tunneling. As a result, the FL phase is destroyed at tem
perature T=0, and a tunneling gap for charge 2e is formed with angular
momentum l not equal 0. We apply our formalism to the U(1) gauge fiel
d coupled to a spinless fermion and find that at T not equal 0 the FL
is again destroyed. We also make some remarks concerning the t-J model
.