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- Thread starter azabak
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Khashishi

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tom.stoer

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Suppose you have fermionic creation and annihilation operators [itex]b_i^\dagger[/itex] and [itex]b_i[/itex] with the usual anti-commutators. Here 'i' is a general index containing all relevant numbers specifying a state like momentum, spin, isospin etc.

The relevant identity which follows from the anti-commutators is

[tex]\left(b_i^\dagger\right)^2 = 0[/tex]

It says that you cannot create a two-particle state with two fermions having both the same state 'i'.

Of course you can construct arbitrary complex interaction terms

[tex]\sum_{ijk, \ldots pqr \ldots}h_{ijk, \ldots pqr \ldots} b_i^\dagger b_j^\dagger b_k^\dagger \ldots b_p b_q b_r \ldots[/tex]

but in all those interactions every diagonal term with (e.g.) i=j vanishes

[tex]h_{iik, \ldots pqr \ldots} b_i^\dagger b_i^\dagger b_k^\dagger \ldots b_p b_q b_r \ldots = 0[/tex]

So the Pauli principle eliminates all these terms from the theory w/o requiring a specific interaction; the number h

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But saying that a physical phenomena is caused by humanly invented algebra is to me not very satisfying explanation. Shouldn't it be more accurate to say that the algebrait holdspurely algebraicallyw/o specifying a dynamics i.e. w/o specifying a Hamiltonian.

Could you say anything about which those more fundamental physical axioms would be? Or alternatively, could it be that the Pauli exclusion principle is a fundamental physical axiom in itself? (meaning that the creation and annihilation operators and their commutators was designed to with the need to fulfill the PEP in mind.)

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tom.stoer

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The Pauli exclusion principle is due to the anti-commutators or Grassmann fields to be used for quantizing fermions; these anti-commutators or Grassmann fields are due to the spin-statistics theorem

Have a look at Wikipedia and references therein: http://en.wikipedia.org/wiki/Spin-statistics_theorem

I have to admit that I am not an expert in axiomatic quantum field theory and that I am not able to comment on formal aspects of these proofs. But up to my knowledge the spin-statistics-theorem is the most fundamental starting point

Have a look at Wikipedia and references therein: http://en.wikipedia.org/wiki/Spin-statistics_theorem

I have to admit that I am not an expert in axiomatic quantum field theory and that I am not able to comment on formal aspects of these proofs. But up to my knowledge the spin-statistics-theorem is the most fundamental starting point

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