- #1
Gregory Gao
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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!
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!
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