# Lorentz Representations

1. Jan 16, 2008

### Marco_84

[SOLVED] Lorentz Representations

I am reading about the Lorentz group on Schweber.
My problem is the following:
I dont really understand how to make the direct product of Representations for this Group.
I know that we need only 2 mubers since the invarints of the gropu are 2.
I know the general reciepie for the SU(n) case is it the same?

Let me ask an example explicity: i've read that Weyl is (1/2,0) Repr and its conjugate is obviously (0,1/2) left handed and right handed; while Dirac is (1/2,1/2).
How can i show that (1/2,0)x(0,1/2)=(1/2,1/2).

The book doesnt go so deep. i think i have to read somewhere else.

marco

2. Jan 17, 2008

### Marco_84

[Never mind i've figured out by myself, it wws just necessary how works complexification for sl(2,C)..

marco

3. Jan 19, 2008

### dextercioby

Did you figure out how $(1/2,0) \otimes (0,1/2) =(1/2,1/2)$ ?

4. Jan 21, 2008

### Marco_84

yeah it is something like this:
(j1,j1')x(j2,j2')=Sum all possible combination of( j,j'). where

j=j1+j2,j1+j2-1,.....,|j1-j2|.
j'=j1'+j2',j1'+j2'-1,.....,|j1'-j2'|.

because after complexification you have that so(1,3) is isomorphic to su(2)xsu(2)....

bye bye