Smooth bosonization. The massive case

Abstract

The (1+1)-dimensional bosonization relations for fermionic mass terms are derived by choosing a specific gauge in an enlarged gauge-invariant theory containing both fermionic and bosonic fields. The fermionic part of the generating functional subject to the gauge constraint can be cast into the form of a strongly coupled Schwinger model, which can be solved exactly. The resulting bosonic theory coupled to the scalar sources then exhibits directly the bosonic counterparts of the fermionic densitiesψψ andψγ 5 ψ.

Smooth non-Abelian bosonization

“…Guided by the experience gained in the abelian case [6], we will derive this gauge-invariant theory by a collective field technique based on a local non-Abelian chiral rotation of fermions [11].…”

“…In the Abelian case [6] this extension of the field space was achieved by introducing a pseudoscalar field via a straightforward chiral transformation of the fermion fields. One can follow the same procedure in this non-Abelian case, but we choose for convenience to depart slightly from this route here, and introduce the fields U(x) by a transformation involving only one chiral component of ψ:…”

“…In ref. [6] we called this phenomenon "anomalous gauge fixing", because in the Abelian case the pertinent gauge fixing turned out to hinge directly on the U(1) anomaly in (1+1) dimensions. Actually, the phenomenon is more general, and not necessarily linked to anomalies.…”

“…The easiest way is to go back to the starting expression in terms of the action (6). Note that a pure non-Abelian phase rotation, ψ → r † ψ ,ψ →ψr , eliminates the coupling to R − at the expense of providing a modified sourceL + :…”

“…It does not seem, however, to lead easily to the kind of generalizations described in ref. [6]. In detail, the difference between the approach known as smooth bosonization and that based on duality can be described as follows.…”