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We discuss how one calculates the coherent path integrals for locallyinteracting systems, where some inconsistencies with exact results have beenreported previously. It is shown that the operator ordering subtlety that ishidden in the local interaction term modifies the Hubbard-Stratonovichtransformation in the continuous time formulation, and it helps reproduce knownresults by the operator method. We also demonstrate that many-body effects inthe strong interaction limit can be well characterized by the free-particletheory that is subject to annealed random potentials and dynamical gauge (orphase) fields. The present treatment expands the conventional paradigm of theone-particle description, and it provides a simple, viable picture for stronglycorrelated materials of either bosonic or fermionic systems.

Exact path-integral evaluation of locally interacting systems: The subtlety of operator ordering