How Does Pauli-Villars Regularization Handle Three Types of Divergences?

[zetafunction]

how does this regularization work ?, suppose we have three kinds of divergencies

$$\Lambda$$ ,..$$log \Lambda$$ and $$\Lambda^{2}$$

then according to Pauli-Villars regularization should we add 3 different and ficticious 'Fields' with Masses A,B,C tending to infinity ??

 

[alalaika]

it actually means that you set a cutoff. when the term you subtract is big enough, you render the integral over the functions finite. in your case I'd say that you have sth like -1/(lambda-A), while A is a very big mass. if lambda is small enough the term won't have any effect on your function but if lambda is bigger than A, the term will have an effect and render your function finite. It is important that A is big but not tending to infinity...