- #1
Niles
- 1,866
- 0
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?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?Niles.
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