[R] interaction of continuous terms

[Irene Mantzouni]

Hi all!
 
this is a rather statistical question:
is it meaningful to consider an interaction effect between 2 continuous covariates?
for example: lm(y~x1+x2+x1:x2) 
Should one of continuous x1, x2 be "transformed" to a categorical variable, i.e. be classified into groups?
Is it easier to interpret the effect if 1 or both are centered to the mean or z-transformed? 
 
Thank you!