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Wave function of two different fermions

  1. Apr 19, 2014 #1
    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! :)
     
  2. jcsd
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