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

The Fourier transform of an inhomogeneous two-point correlation function, in space and Euclidean time, is derived for a limited number of spin polarized fermions in an external potential. The formulation is based on the many-body generalization of the Feynman–Kac functional. Special attention is given to the finite number aspects and the implications thereof for the fugacity. An analysis of the correlation function in terms of single-particle propagators is obtained, leading to an occupation function representation. For the harmonic model, the temporal Fourier components of the two-point correlation matrix are worked out in the low-temperature limit.