Loop Corrections and Bosonization Formulae

TL;DR

This paper investigates the role of loop corrections in the path integral bosonization process for higher-dimensional theories, showing that higher-order loops cancel out under consistent approximation schemes.

Contribution

It demonstrates that loop corrections can be consistently ignored in the bosonization functional integral when treated uniformly in both fermionic and bosonic representations.

Findings

Higher-order loop contributions cancel out in the generating functional.

Consistent approximation of loop expansions simplifies the bosonization process.

Loop corrections are negligible if treated symmetrically in fermionic and bosonic integrals.

Abstract

We study the functional integrals that appear in a path integral bosonization procedure for more than two spacetime dimensions. Since they are not in general exactly solvable, their evaluation by a suitable loop expansion would be a natural procedure, even if the exact fermionic determinant were known. The outcome of our study is that we can consistently ignore loop corrections in the functional integral defining the bosonized action, if the same is done for the functional integral corresponding to the bosonic representation of the generating functional. If contributions up to some order $l$ in the number of loops are included in both integrals, all but the lowest terms cancel out in the final result for the generating functional.