Noether current for exchange symmetry

  • Thread starter Ravi Mohan
  • Start date
  • #1
196
19
In Quantum Mechanics, when we exchange identical particles the physics doesnt 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.
 

Answers and Replies

  • #2
DrDu
Science Advisor
6,234
885
That's not a discrete symmetry so Noether's theorem is not applicable and there is no infinitesimal generator which is conserved.
 
  • #3
Dale
Mentor
Insights Author
2021 Award
32,752
9,853
That's not a discrete symmetry so Noether's theorem is not applicable
I think you mean "That's not a differentiable symmetry ..."
 
  • #4
196
19
Ok got it. Thanks.
I find this helpful too
http://ajp.aapt.org/resource/1/ajpias/v64/i7/p840_s3?isAuthorized=no [Broken]
 
Last edited by a moderator:
  • #5
244
49
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
 
  • #6
DrDu
Science Advisor
6,234
885
I think you mean "That's not a differentiable symmetry ..."

Of course, thanks!
 
  • #7
DrDu
Science Advisor
6,234
885
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.
 
  • #8
196
19
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?
 
  • #9
DrDu
Science Advisor
6,234
885
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.
 

Related Threads on Noether current for exchange symmetry

Replies
12
Views
6K
Replies
6
Views
2K
Replies
19
Views
9K
Replies
5
Views
2K
  • Last Post
Replies
3
Views
1K
Replies
33
Views
9K
Replies
6
Views
2K
  • Last Post
Replies
6
Views
2K
Top