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- Thread starter Gravitonion
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Ken G

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tom.stoer

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Are you familiar with the harmonic oscillator?

Fermionic creation and annihilation operators are constructed using anti-commutators (instead of commutators

[tex]\{b_s,b^\dagger_{s^\prime}\} = \delta_{s\,s^\prime}[/tex]

[tex]\{b_s,b_{s^\prime}\} = \{b^\dagger_s,b^\dagger_{s^\prime}\} = 0[/tex]

The last equation is important b/c for s=s' it can be rewritten as :

[tex](b^\dagger_s)^2 = 0[/tex]

s,s' represent the quantum numbers

You can construct a states where each s, s', s'', ... is occupied by either zero or one particle. But if you want to construct a state with two particles sitting in state s you get

[tex]|2s\rangle = (b^\dagger_s)^2|0\rangle = 0[/tex]

due to the anticommutator.

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They can be in the same state as long as they have different positions though right?

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tom.stoer

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Sorry, I forgot to explain that creation and annihilation operators act in momentum space and that this means that s is a collection of momentum, spin, isospin, etc.}. Therefore they are not located anywhere in position space.They can be in the same state as long as they have different positions though right?

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