- #1

RedX

- 970

- 3

1) You begin with your original Lagrangian, and you want to construct an effective Lagrangian out of it.

2) You redefine your coupling constants in your original Lagrangian so that they include the integral from a cutoff to infinity (i.e., you combine the higher order corrections into the coupling constants, but only from the cutoff to infinity). This way, when you make an effective Lagrangian, you no longer need to integrate to infinity, since this was already done in the coupling constants.

3) Step 2 isn't perfect for some reason (why?), so your effective Lagrangian needs to include not just a redefinition of the coupling constants in your original Lagrangian, but new terms (an infinite amount of them) whose coupling can have negative mass dimensions.

4) As of yet all your parameters are undefined - you didn't specify a mass scale or anything. You decide that the mass scale is the cutoff. At this point you could determine the value of all your parameters evaluated at the cutoff by comparing to experiment?

5) Now you integrate below your cutoff, and in doing so you derive a renormalization group equation for all your coupling constants.

6) Now you're done and can see how parameters in your effective Lagrangian changes as you vary the cutoff.

What's the point of all this? What's this used for that regular renormalization can't do?