The polarization function of a finite number of confined spin polarized fermions

The Fourier transform of an inhomogeneous two-point correlation function, i n space and Euclidean time, is derived for a limited number of spin polariz ed fermions in an external potential. The formulation is based on the many- body generalization of the Feynman-Kac functional. Special attention is giv en to the finite number aspects and the implications thereof for the fugaci ty. An analysis of the correlation function in terms of single-particle pro pagators is obtained, leading to an occupation function representation. For the harmonic model, the temporal Fourier components of the two-point corre lation matrix are worked out in the low-temperature limit. (C) 2001 Elsevie r Science Ltd. All rights reserved.