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.

 

[jeff]

No, but from the modern effective field theoretic perspective, because higher order terms are suppressed relative to lower order ones, it's perfectly alright to calculate to whatever order in the coupling you want by employing different counterterms in each subtraction.