SEMICLASSICAL APPROACH FOR NONRELATIVISTIC FERMIONS IN LOW DIMENSIONS

We present a collective field formalism for nonrelativistic fermions in one spatial dimension. A bosonization technique is used to convert the quantum mechanical fermionic problem to a bosonic one, which is further described as a second quantized Schrodinger field theory. A formulation in terms of current and density variables gives rise to the collective field representation. Applications of our formalism to the D = 1 Hermitian matrix model and the system of one-dimensional fermions in the presence of a weak electromagnetic field are discussed.