Abstract
Abstract We study relativistic anyon field theory in 1+1 dimensions. While (2+1)-dimensional anyon fields are equivalent to boson or fermion fields coupled with the Chern–Simons gauge fields, (1+1)-dimensional anyon fields are equivalent to boson or fermion fields with many-body interaction. We derive the path integral representation and perform a lattice Monte Carlo simulation.
Highlights
The exotic particle obeying fractional statistics or interpolating a boson and a fermion is called the anyon [1–3]
The field theoretical description of the (2+1)-dimensional anyon has been well understood. It is given by ordinary boson or fermion fields coupled with the Chern-Simons gauge fields
Even if non-interacting anyon field theory is considered, it is equivalent to interacting gauge theory with a variety of quantum phenomena
Summary
The exotic particle obeying fractional statistics or interpolating a boson and a fermion is called the anyon [1–3]. The field theoretical description of the (2+1)-dimensional anyon has been well understood. It is given by ordinary boson or fermion fields coupled with the Chern-Simons gauge fields. Since anyons in other dimensions are novel quantum states, their physical properties are fascinating subjects. (1+1)-dimensional anyons and its experimental realization have been intensively discussed in non-relativistic physics [22–38]. The study of (1+1)-dimensional relativistic anyons has been limited in quantum mechanics [39, 40]. We study the relativistic version of anyon field theory in 1+1 dimensions. The simulation of the (1+1)-dimensional anyon field theory is much easier than the (2+1)-dimensional one, even though it has the sign problem, as shown in this paper
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