Abstract
We review some unusual facts about the theory of non-relativistic anyons in 2+1 dimensions, and use it as a laboratory to explore how interesting features of nonrelativistic field theory correspond to those of many-body quantum mechanics. In particular, we offer an explanation of how Jackiw-Pi vortices arise as the classical limit of certain many-body states in the quantum mechanical theory. Along the way, we make various interesting observations about universal features of the spectrum of anyons subject to different amounts of tuning.
Highlights
As we will explain in this extended introduction, these operators reveal that there is something special about theories of anyons experiencing attractive contact interactions
We review some unusual facts about the theory of non-relativistic anyons in 2+1 dimensions, and use it as a laboratory to explore how interesting features of nonrelativistic field theory correspond to those of many-body quantum mechanics
We offer an explanation of how Jackiw-Pi vortices arise as the classical limit of certain many-body states in the quantum mechanical theory
Summary
That it is convenient to instead define a bosonic wavefunction ψ = e−iθ/kψ It follows that the action of the usual ‘free’ Hamiltonian on ψ is given by. Note that there are two special points at which no dimensionful parameter is needed to describe the theory: R0 = 0 and R0 = ±∞, corresponding to boundary conditions ψ ∼ r1/k and ψ ∼ r−1/k respectively. At these points, the theory is scale-invariant, which imbues it with a lot of extra structure, namely the SO(2, 1) symmetry of conformal quantum mechanics [6]. There is always a bound state ψ(r) ∝ K0(r/R0) for any non-trivial R0
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