Express arbitrary state in second quantization

[daudaudaudau]

How do I express an arbitrary 2-particle state in second quantization? I could write this
$$|\psi\rangle=\sum_{mn}c_{mn} a_m^\dagger a_n^\dagger |0\rangle$$
where $c_{mn}$ is a constant, $a_n^\dagger$ is the creation operator and $|0\rangle$ is the vacuum state. The only problem is that I want to sum over all PAIRS, and when I write the sum like this, all pairs are included twice, which is a mess.

 

[arkajad]

Well, you did not specify the statistics (Bose, Fermi, distinguishable particles?).

 

[daudaudaudau]

Fermi.

 

[arkajad]

Then it is enough to take m<n (because of the anticommutation).