Noether current for exchange symmetry

[Ravi Mohan]

In Quantum Mechanics, when we exchange identical particles the physics doesn't change. I wonder what stuff is conserved when this symmetry is demanded.
I asked my professor but he didnt/couldnt answer. Google is no help either.

 

[DrDu]

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

 

[Dale]

That's not a discrete symmetry so Noether's theorem is not applicable

I think you mean "That's not a differentiable symmetry ..."

 

[Ravi Mohan]

Ok got it. Thanks.
I find this helpful too
http://ajp.aapt.org/resource/1/ajpias/v64/i7/p840_s3?isAuthorized=no

 

[Jazzdude]

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

 

[DrDu]

I think you mean "That's not a differentiable symmetry ..."

Of course, thanks!

 

[DrDu]

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

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

 

[Ravi Mohan]

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

I would like to read that paper. Can you give the link?

 

[DrDu]

I would like to read that paper. Can you give the link?

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