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## Main Question or Discussion Point

Hi

Say I have the following two fermionic creation/annihilation operators

[tex]

c^\dagger_ic_j

[/tex]

1) Yesterday, my lecturer said that the following is valid

[tex]

c^\dagger_ic_j = \delta_{i,j}c_jc^\dagger_i

[/tex]

Can you guys explain to me, where this formula comes from? I originally thought that it was one of the anti-commutator relations, but it cannot come from there.

2) Say I have en expression of the form

[tex]

c_{k+q}^\dagger c_{k-q'} c^\dagger_{k'-q'}c_{k'}

[/tex]

If the operators are fermionic, then if I want to have all dagger-operators on the LHS and non-dagger operators on the RHS, then do I have to use anti-commutator relatations in order to rewrite the expression?

Likewise, if they were bosonic operators, then I would have to use commutator relations in order to rewrite the expression?

Best,

Niles.

Say I have the following two fermionic creation/annihilation operators

[tex]

c^\dagger_ic_j

[/tex]

1) Yesterday, my lecturer said that the following is valid

[tex]

c^\dagger_ic_j = \delta_{i,j}c_jc^\dagger_i

[/tex]

Can you guys explain to me, where this formula comes from? I originally thought that it was one of the anti-commutator relations, but it cannot come from there.

2) Say I have en expression of the form

[tex]

c_{k+q}^\dagger c_{k-q'} c^\dagger_{k'-q'}c_{k'}

[/tex]

If the operators are fermionic, then if I want to have all dagger-operators on the LHS and non-dagger operators on the RHS, then do I have to use anti-commutator relatations in order to rewrite the expression?

Likewise, if they were bosonic operators, then I would have to use commutator relations in order to rewrite the expression?

Best,

Niles.

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