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Many particle wave-functions to me have a very confusing methodology. I've been taught some procedure for creating wave functions that are symmetric or anti-symmetric upon exchange of coordinates.

I really struggle to understand how this comes about as a result of typical quantum mechanics. And often when see work that deals with multiple particles, I don't see any need for this type of methodology.

Is it possible that these rules about symmetry upon exchange can be explained by first principles? For example, the Hong-ou-mandel effect involves interference of bosons, but this "symmetric/antisymmetric" stuff is not typically invoked when discussing it. But it should be connected since its a multiparticle effect, right?

So overall: I'm looking to see if there are methods of finding "symmetric & antisymmetric" wavefunctions of fermions & bosons that can be explained by first principles (such as interference effects of multiparticle states).

Qmechanic
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Steven Sagona
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    Have you already read about the spin statistics theorem? That is the basic theorem which addresses your question. – KF Gauss Jun 03 '22 at 00:09
  • As commented above, these first principles are those of quantum field theory: positive norm states in the Hilbert space, Lorentz invariance, and positive energy demand the statistics seen in Nature. The only exceptions are ghosts (coming from gauge fixing), but their physicality is restricted to canceling the unphysical gauge boson polarizations. – Vinicius Névoa Jun 03 '22 at 01:21

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