# Antisymmetry in fermionic Fock space

• A
Dear all,

When we annihilate a particle at level ##k## in fermionic Fock space we use the relation
$$\hat{c}_k| \dots, 1_k, \dots \rangle = (-1)^{\sum_{i=1}^{k-1} n_i}|\dots,0_k,\dots\rangle.$$

Where the factor (##\pm1##) depends on the occupation numbers of all the levels below the level ##k##.
However, I do not see what the link is between antisymmetry when permuting two electrons, i.e.
$$\hat{c}_n^\dagger\hat{c}_m^\dagger|0\rangle = -\hat{c}_m^\dagger\hat{c}_n^\dagger|0\rangle,$$
and how this is incorporated by counting the number of electrons below level ##k##.

Ian

Last edited:

## Answers and Replies

Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.