Wave function of two different fermions

  • Thread starter Marchigno
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Hi! According to quantum field theory, must the wave function of two different fermions be antisymmetric?
If I have a state of two equal fermions: [tex]b^\dagger(p_1)b^\dagger(p_2)|0>[/tex] I can construct the general state of two fermions:
[tex]\int d^3p_1 d^3p_2f(p_1,p_2)b^\dagger(p_1)b^\dagger(p_2)|0>[/tex]
where f is the wave function. Now because [tex]\{b^\dagger(p_1),b^\dagger(p_2)\}=0[/tex]
the wave function f mast be antisymmetric.
The question is: if I now consider two different fermions: [tex]b^\dagger(p_1)d^\dagger(p_1)|0>[/tex]
so that the general state is
[tex]\int d^3p_1 d^3p_2f(p_1,p_2)b^\dagger(p_1)d^\dagger(p_2)|0>[/tex]
because
[tex]\{b^\dagger(p_1),d^\dagger(p_2)\}=0[/tex]
remains true, does it mean the wave function of any two fermions will be antisymmetric? I thought it was true only for two identical particles!
Thank you for the answers! :)
 

DrClaude

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If the fermion are not identical, then there is no possible symmetry to start with, so the Pauli principle does not apply.
 

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