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Fermion creation op anticommutator relations

  1. Nov 10, 2007 #1
    1. The problem statement, all variables and given/known data
    2. Relevant equations
    Given is
    [tex]c_p = \sum_{n_i} (-1)^{N_p}|...,n_p=0,...><...,n_p=1,...|[/tex]
    [tex]c_p^{\dagger} = \sum_{n_i} (-1)^{N_p}|...,n_p=1,...><...,n_p=0,...|[/tex]
    [tex]N_p = \sum_{i=1}^{p-1}n_i[/tex]

    Verify
    [tex]\{c_p,c_q\} = \{c_p^{\dagger},c_q\} = \{c_p^{\dagger},c_q^{\dagger}\} = 0[/tex]
    [tex]\{c_p^{\dagger},c_p\} = 1[/tex]

    3. The attempt at a solution

    If we let the commutator [tex]\{c_p,c_q\}[/tex] act on some state, any state where [tex]n_p[/tex] or [tex]n_q[/tex] are zero will just give zero back. If [tex]n_p[/tex] and [tex]n_q[/tex] are one, then both [tex]c_p c_q[/tex] and [tex]c_q c_p[/tex] puts zeros there and give a factor [tex](-1)^{N_p+N_q}[/tex] in front. I can't see where any sign change comes from.
     
  2. jcsd
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