Normal ordering for bosons vs fermions

  • #1
planetology
13
0
Why is it that when normal ordering the terms in the Hamiltonian for bosons, the commutation rules are ignored, but when normal ordering fermion operators the anti-commutation rules are used to justify a change in sign?
 

Answers and Replies

  • #2
quantumdude
Staff Emeritus
Science Advisor
Gold Member
5,575
23
I remember thinking about this a few years ago, and I seem to remember the answer was in the fact that the negative sign canceled with another negative sign, giving the appearance that we ignore the rule.

Here is an easy-to-read document that will be of some assistance:

http://xxx.lanl.gov/pdf/physics/0212061

I will get back to this later with a more definitive post.
 
  • #3
planetology
13
0
Originally posted by Tom


Here is an easy-to-read document that will be of some assistance:

http://xxx.lanl.gov/pdf/physics/0212061

I will get back to this later with a more definitive post.

Thanks, that paper is a really good one. I have not gotten all the way through it yet so don't know if it answers the main question, but very useful in any case.
 
  • #4
quantumdude
Staff Emeritus
Science Advisor
Gold Member
5,575
23
OK, I re-read the paper, and it only states the reason for ignoring the commutation rules for the harmonic oscillator potential. The reason is that the only effect is to shift the energy eigenvalues by (1/2)hf. In other words, the physics is unchanged (because only energy differences are measurable).

So, I think that gives us a lead for why we don't ignore it for fermions: something more happens than a mere shift in the energies.

That would be the next thing to look into, I think.
 

Suggested for: Normal ordering for bosons vs fermions

  • Last Post
Replies
5
Views
1K
Replies
31
Views
917
Replies
50
Views
1K
  • Last Post
Replies
12
Views
1K
  • Last Post
Replies
5
Views
728
  • Last Post
Replies
5
Views
1K
Replies
4
Views
811
Replies
3
Views
4K
  • Last Post
Replies
5
Views
1K
  • Last Post
Replies
9
Views
1K
Top