  We establish a correspondence between the resummation of world lines and the
diagonalization of the Hamiltonian for a strongly correlated electronic system.
For this purpose, we analyze the functional integrals for the partition
function and the correlation functions invoking a slave boson representation in
the radial gauge. We show in the spinless case that the Green's function of the
physical electron and the projected Green's function of the pseudofermion
coincide. Correlation and Green's functions in the spinful case involve a
complex entanglement of the world lines which, however, can be obtained through
a strikingly simple extension of the spinless scheme. As a toy model we
investigate the two-site cluster of the single impurity Anderson model which
yields analytical results. All expectation values and dynamical correlation
functions are obtained from the exact calculation of the relevant functional
integrals. The hole density, the hole auto-correlation function and the Green's
function are computed, and a comparison between spinless and spin 1/2 systems
provides insight into the role of the radial slave boson field. In particular,
the exact expectation value of the radial slave boson field is finite in both
cases, and it is not related to a Bose condensate.
