One Dimensional Anomaly of the Fermi Surface

Abstract

Consider a N-fermions system with hamiltonian, see [1]:

$$H = \sum\limits_{i = 1}^N {{{ - {\Delta _{xi}} - p_F^2} \over {2m}}} + \lambda \sum\limits_{i < j} {v({x_i}} - {x_j})$$

((1))

where m,p _F are two fixed parameters, λ is the coupling constant and v is the pair potential, supposed smooth and with short range p ⁻¹₀ .