2
$\begingroup$

There are at least two ways to compute the electron-self energy. You can use Pauli-Villars or dimensional regularization, for example.

On Weinberg's book, it's chosen the first method, while on my lectures note the second.

My question is: in general, after adding the Pauli-Villars regulator, can I extend the dimension of the integral to $d$-dimensions? I've done the calculations in this way and I got the same result.

Is it correct?

$\endgroup$
2
$\begingroup$

It seems that you can use them together because of one simple reason: the Pauli-Villars regularization provides changing of definition of the Green functions and leaves the procedure of integration unchanged, while dimensional regularization provides changing of the procedure of integration without changing of the definition of the Green functions. Note that these regularization schemes break different symmetries in gauge theories: the first one breaks gauge symmetry, while the second one breaks chiral symmetry. In theories like QED you may use Pauli-Villars regularization when you don't need to compute quantities like vacuum polarization.

You may work with different cut-offs, and proceed limits independently.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.