Today in class, by the existence of an operator that exchanges the states of two indistinguishable particles, we attempted to derive the existence of fermions and bosons & how this relates to the symmetries of multiparticle wave functions.(adsbygoogle = window.adsbygoogle || []).push({});

The argument given in my textbook is: define an exchange operator P. "Clearly" P^2 = I. Therefore, the eigenvalues of P are +1 and -1. Systems of identical particles are eigenvectors of an exchange operator, so they are therefore either symmetric or antisymmetric under exchange of particles.

On the other hand, I don't see why we need P^2 = I. We can have P^2 = e^(i theta) for any value of theta because the only requirement we have is that exchanging twice leaves us with a state that is physically indistinguishable.

So what gives? Is the argument given in my book completely bogus? Can someone direct me to another book that has an explanation of bosons & fermions? (I'm looking at Townsend by the way)

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# Exchange Operators & Spin Statistics - I don't the conclusions

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