Can the coupling constant change?

eljose79
In fact let,s supose we have a lagrangian of the type

L=L0+gLInt where "g" is the coupling constant,..but unfortunately could happen that due to the dimension of g the theory would not be renormalizable...

my question if that if there would be a chance of doing a canonical transformation so we can change the coupling constant to another g' so that the theory would become renormalizable..is possible?..if it is how would it do?.

Another chance i think is to add a four-divergence term depending on the fields and momenta so we have

L´=L0+gLint+F due to that F is a four divergence the lagrangian L´will be equivalent to the L now the trick would be to set

gLint+F=0 as a condition or constraint.