  This short note was born out of discussions on anyons in the FQHE at the YITP
workshop "Fundamental problems of quantum field theories" (December 19-21,
2001, YITP, Kyoto). At that time, I felt that there might not be a sound
consensus of opinion on the subject. Now, I would like to show my understanding
here, the essential part of which is based on hep-th/0110197.
  The first problem discussed is a notion of ``bosonized electrons
(bosonization)", which are unphysical objects from the standpoint of the
Chern-Simons gauge invariance. Therefore, their condensate is merely of
mathematical concept and the true physical state realized is a liquid-like one
made of degeneration of anyons. Based on this recognition, I argue about a
mechanism of the degeneration that results from the genuine CS gauge field
theory. It is noted that the Ginzburg-Landau effective theory is not necessary.
As the last problem, the gauge invariance in the "composite-fermion theories"
is discussed.
