### 6.5 Inﬁnities and
renormalisation

One of the key features missing in the
discussion above is the fact that all the pictures I have drawn
are inﬁnite – somewhat of a severe blow. The key
point is to understand that this is not a problem, but has to
do with a misinterpretation of the series.

When we introduce
$\alpha $ and
$e$ in our theory these we use the measured value of the
charge of an electron – which is a solution to the full
theory, not to the artiﬁcial problem with all vacuum
ﬂuctuations turned of. What it means is that we should
try to express all our answers in physically sensible
(measurable) quantities. Renormalisation is the mathematical
procedure that does this. A theory (such as QED) is called
renormalisable if we can make all expressions ﬁnite by
re-expressing them in a ﬁnite number of physical
parameters.