Normal ordering for bosons vs fermions

[planetology]

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?

[Tom Mattson]

I remember thinking about this a few years ago, and I seem to remember the answer was in the fact that the negative sign cancelled 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.

[planetology]

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.

[Tom Mattson]

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.