Quantum Description of Anyons: Role of Contact Terms

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.