Quantum Description of Anyons: Role of Contact Terms

TL;DR

This paper rigorously connects nonrelativistic Chern-Simons quantum field theory with first-quantized descriptions of anyons, clarifying the role of contact terms and establishing a solid theoretical foundation.

Contribution

It provides an all-order analysis linking field theory contact terms to Hamiltonian self-adjoint extensions in the first-quantized framework for nonrelativistic anyons.

Findings

Clarifies the role of contact terms in renormalized perturbation theory

Establishes a precise correspondence between field theory and first-quantized descriptions

Provides a rigorous foundation for quantum field theories of nonrelativistic anyons

Abstract

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.