5
$\begingroup$

For two particles, $\langle {\mathcal T} a(t_1) a^\dagger (t_2) \rangle = \langle a(t_1) a^\dagger (t_2)\rangle \theta (t_1-t_2) + \xi \langle a^\dagger (t_2)a(t_1) \rangle \theta (t_2-t_1)$ with $\xi$ is a plus sign for bosons and a minus sign for fermions.

How would I write, for example, $\langle {\mathcal T} a(t_1) a^\dagger (t_2) a(t_3) a^\dagger (t_4) \rangle$ ?

$\endgroup$
1

1 Answer 1

4
$\begingroup$

Just sum over each permutation of [1,2,3,4], for each permutation $[I_1,I_2,I_3,I_4]$you would have a factor of $\theta(t_{I_1}-t_{I_2})\theta(t_{I_2}-t_{I_3})\theta(t_{I_3}-t_{I_4})$ times the corresponding operator product, etc.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

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