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: b^\dagger(p_1)b^\dagger(p_2)|0> I can construct the general state of two fermions:
\int d^3p_1 d^3p_2f(p_1,p_2)b^\dagger(p_1)b^\dagger(p_2)|0>...
I was wondering...if I have a spinor or a vector field, this means that the vacuum state cannot be invariant under a Lorentz transformation? So if I have no fermions in a reference system, I could have a fermion in another system? Thank you.