Noether current for exchange symmetry

That's not a discrete symmetry so Noether's theorem is not applicable and there is no infinitesimal generator which is conserved.

 

It should be possible to formulate the exchange symmetry in terms of a continuous and differentiable unitary group, by means of mixing the particles instead of exchanging them entirely. Of course you'd have to do it in a way that recovers the discrete symmetry for a certain mixing angle.

Cheers,

Jazz

 

Of course, thanks!

 

I remember having seen in American Journal of Physics an explicit construction of the exchange operator in terms of x and p.

 

I fear not as I no longer have access to Am J Phys.