0
$\begingroup$

How do I evaluate the anti-commutator of $\frac{\partial}{\partial\chi}$ and $\frac{\partial}{\partial\eta}$ when both $\chi$ and $\eta$ are Grassmann variables?

$\endgroup$
  • 1
    $\begingroup$ ... act with them on an arbitrary function and see what happens? $\endgroup$ – AccidentalFourierTransform May 5 at 17:32
0
$\begingroup$

As user AccidentalFourierTransform writes in a comment: Act with them on an arbitrary function and see what happens...

More generally, one may show that derivatives of supernumbers $z$ and $w$, with definite Grassmann parities $|z|$ and $|w|$, resectively, supercommute: $$ \frac{\partial}{\partial z}\frac{\partial}{\partial w}~=~(-1)^{|z||w|}\frac{\partial}{\partial w}\frac{\partial}{\partial z} .$$

$\endgroup$

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.