# Pseudoparticle approach

1. Nov 4, 2014

### Gregory Gao

Hi all,

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 $\{|S\rangle\}$, here $S$ represents both particle number and level. Pseudoparticle approach says that these states are generated from a pseudoparticle vacuum with $p^{\dagger}_S$, i.e., $p^{\dagger}_S|PPV\rangle=|S\rangle$. Also, sine the Fock space is complete, the condition that $\sum_{Ni}|Ni\rangle\langle Ni|=I$ is just $\sum_{S}p^{\dagger}_Sp_S=I$ 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!

Last edited: Nov 4, 2014
2. Nov 9, 2014