Bosonization of $QED_3$ with an induced Chern - Simons term

TL;DR

This paper extends the bosonization of 2+1 dimensional QED to include an induced Chern-Simons term, resulting in a Lorentz-invariant bosonic theory with Maxwell's equations, revealing new operator algebra features.

Contribution

It introduces a bosonization scheme for QED in 2+1 dimensions with a quantized Chern-Simons term, generalizing previous work to include topological effects.

Findings

Bosonic theory is Lorentz invariant in the continuum limit.

Maxwell's equations emerge as equations of motion.

Operator algebra exhibits nontrivial mixing with lower dimensional operators.

Abstract

We extend the bosonization of $2+1$ - dimensional QED with one fermionic flavor performed previously to the case of QED with an induced Chern - Simons term. The coefficient of this term is quantized: $e^2n/8\pi$, $n\in {\bf Z}$. The fermion operators are constructed in terms of the bosonic fields $A_i$ and $E_i$. The construction is similar to that in the $n=0$ case. The resulting bosonic theory is Lorentz invariant in the continuum limit and has Maxwell's equations as its equations of motion. The algebra of bilinears exhibits nontrivial operatorial mixing with lower dimensional operators, which is absent for $n=0$.