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We make an all-order analysis to establish the precise correspondence betweennonrelativistic Chern-Simons quantum field theory and an appropriatefirst-quantized description. Physical role of the field-theoretic contact termin the context of renormalized perturbation theory is clarifed through theirconnection to self-adjoint extension of the Hamiltonian in the first-quantizedapproach. Our analysis provides a firm theoretical foundation on quantum fieldtheories of nonrelativistic anyons.Comment: 27 pages and 7 figure

Quantum description of anyons: Role of contact terms