Clebsch-Gordan in Fock Space?

  • Thread starter lugita15
  • Start date
  • #1
1,554
15
When adding the angular momenta of two particles, you use Clebsch-Gordan coefficients, which allow you, in fancy language, to decompose the tensor product of two irreducible representations of the rotation group into a direct sum of irreducible representations. (I'm not exactly clear on what this means, so on a side note can someone suggest a good book on representation theory of Lie groups?)

If we want to add the angular momenta of even more particles, then we have to use other coefficients, like the Wigner 3j, 6j, or in general 3nj symbol. But what if you have an unknown number of particles, like you do in quantum field theory? In this case quantum states live in a so-called Fock space made of a direct sum of infinitely many tensor products of Hilbert spaces (which is another thing I'm unclear on). So then how do you add angular momentum in Fock space? To put it another way, how do you decompose a tensor product of irreducible representations into a direct sum if you have a variable number of terms in the tensor product?

Any help would be greatly appreciated.
Thank You in Advance.
 
Last edited:

Answers and Replies

Related Threads on Clebsch-Gordan in Fock Space?

  • Last Post
Replies
1
Views
743
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
5
Views
3K
  • Last Post
Replies
2
Views
3K
  • Last Post
Replies
5
Views
7K
Replies
1
Views
412
Replies
3
Views
1K
Replies
3
Views
3K
Replies
3
Views
360
Replies
6
Views
3K
Top