- #1
bartadam
- 41
- 0
I'm very very very confused and extremely thick.
If [itex] \Lambda_i [/itex] is some element of the Lorentz group and [itex] \Lambda_j [/itex] is another, different element of the group then under multiplication...
[itex] \Lambda_i \Lambda_j [/itex] is also an element of the Lorentz group, say
[itex] \Lambda_i \Lambda_j =c_{ij}^k\Lambda_k[/itex]
where [itex] c_{ij}^k [/itex] has value 1 for one unique combination of i,j and k and 0 for the others and with a sum over k.
Now I appreciate the i,j and k should be continuous but for the moment assume they are discrete because it's easier. i,j and k run over all the integers because there are infinitely many elements of the group.
How the hell do I find the [itex] c_{ij}^k [/itex]? I have absolutely no idea. My knowledge of rep theory is **** poor.
If [itex] \Lambda_i [/itex] is some element of the Lorentz group and [itex] \Lambda_j [/itex] is another, different element of the group then under multiplication...
[itex] \Lambda_i \Lambda_j [/itex] is also an element of the Lorentz group, say
[itex] \Lambda_i \Lambda_j =c_{ij}^k\Lambda_k[/itex]
where [itex] c_{ij}^k [/itex] has value 1 for one unique combination of i,j and k and 0 for the others and with a sum over k.
Now I appreciate the i,j and k should be continuous but for the moment assume they are discrete because it's easier. i,j and k run over all the integers because there are infinitely many elements of the group.
How the hell do I find the [itex] c_{ij}^k [/itex]? I have absolutely no idea. My knowledge of rep theory is **** poor.