  We make an all-order analysis to establish the precise correspondence between
nonrelativistic Chern-Simons quantum field theory and an appropriate
first-quantized description. Physical role of the field-theoretic contact term
in the context of renormalized perturbation theory is clarifed through their
connection to self-adjoint extension of the Hamiltonian in the first-quantized
approach. Our analysis provides a firm theoretical foundation on quantum field
theories of nonrelativistic anyons.
