On Abelian bosonization of free fermi fields in three space dimensions

Tiefeng Xu, Feng Chen, Wenzhou Li

Ramesh Abhiraman, Charles M. Sommerfield

One of the methods used to extend two-dimensional bosonization to four space-time dimensions involves a transformation to new spatial variables so that only one of them appears kinematically. The problem is then reduced to an Abelian version of two-dimensional bosonization with extra ``internal'' coordinates. On a formal level, putting these internal coordinates on a finite lattice seems to provide a well-defined prescription for calculating correlation functions. However, in the infinite-lattice or continuum limits, certain difficulties appear that require very delicate specification of all of the many limiting procedures involved in the construction.

Edward Witten

J. C. Le Guillou, Carlos Núñez, F Schaposnik +1 more

We consider the fermion-boson mapping in three dimensional space-time, in the Abelian case, from the current algebra point of view. We show that in a path-integral framework one can derive a general bosonization recipe leading, in the bosonic language, to the correct equal-time current commutators of the original free fermionic theory.

Edward Witten

Carlos Núñez

We consider the fermion-boson mapping in three dimensional space-time, in the Abelian case, from the current algebra point of view. It is shown that in a path-integral framework one can derive a general bosonization recipe leading, in the bosonic language, to the correct equal-time current commutators of the original free fermionic theory.