  A study for checking validity of the auxiliary field method (AFM) is made in
quantum mechanical four-fermi models which act as a prototype of models for
chiral symmetry breaking in Quantum Electrodynamics. It has been shown that
AFM, defined by an insertion of Gaussian identity to path integral formulas and
by the loop expansion, becomes more accurate when taking higher order terms
into account under the bosonic model with a quartic coupling in 0- and
1-dimensions as well as the model with a four-fermi interaction in 0-dimension.
The case is also confirmed in terms of two models with the four-fermi
interaction among $N$ species in 1-dimension (the quantum mechanical four-fermi
models): higher order corrections lead us toward the exact energy of the ground
state. It is found that the second model belongs to a WKB-exact class that has
no higher order corrections other than the lowest correction. Discussions are
also made for unreliability on the continuous time representation of path
integration and for a new model of QED as a suitable probe for chiral symmetry
breaking.
