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I have a question which bugs me forever. Anyone happens to know about pseudoparticle approach?

In many-particle physics, suppose we have a many particle hamiltonian which has eigenstates in Fock space, i.e., with 0, 1, 2, 3, ... electrons, denoted by [itex]\{|S\rangle\}[/itex], here [itex]S[/itex] represents both particle number and level. Pseudoparticle approach says that these states are generated from a pseudoparticle vacuum with [itex]p^{\dagger}_S[/itex], i.e., [itex]p^{\dagger}_S|PPV\rangle=|S\rangle[/itex]. Also, sine the Fock space is complete, the condition that [itex]\sum_{Ni}|Ni\rangle\langle Ni|=I[/itex] is just [itex]\sum_{S}p^{\dagger}_Sp_S=I[/itex] in the pseudoparticle language.

I can understand this, but people are claiming "pseudoparticle operator is fermionic if it corresponds to a state with an odd number of fermions, bosonic if it corresponds to a state of an even number of fermions". And they claim this is derived from the property that electrons are fermions.

Could someone help give a detailed explanation on the fermion/boson property of pseudoparticle operator? Hard proof by formulation is preferred.

Thank you in advance!

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# Pseudoparticle approach

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