  We show in a precise way, either in the fermionic or its bosonized version,
that Bose symmetry provides a systematic way to carry out the chiral
decomposition of the two dimensional fermionic determinant. Interpreted
properly, we show that there is no obstruction of this decomposition to gauge
invariance, as is usually claimed. Finally, a new way of interpreting the
Polyakov-Wiegman identity is proposed.
