We make an all-order analysis to establish the precise correspondence between nonrelativistic Chern-Simons quantum field theory and an appropriate first-quantized description. The physical role of the field-theoretic contact term in the context of renormalized perturbation theory is clarified through their connection to the 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.

• Received 3 June 1996

DOI:https://doi.org/10.1103/PhysRevD.55.2227