  We have addressed the issue of field redefinition in connection with
renormalisability. Our study is restricted to theories of interacting scalar
fields. We have, in particular, shown that if a theory is renormalisable in the
usual power-counting sense then it remains renormalisable in the same sense
after a change of variables. This is due to the use of the powerful method of
the background field expansion. In the case of a single complex sclar field, it
turns out that the determination of the counter-terms is much simpler when
polar coordinates are used. We illustate this by carrying out a one-loop
calculation in the latter case.
