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Lorentz Representations

  1. Jan 16, 2008 #1
    [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.

    thanks in advance
    marco
     
  2. jcsd
  3. Jan 17, 2008 #2
    [Never mind i've figured out by myself, it wws just necessary how works complexification for sl(2,C)..

    marco
     
  4. Jan 19, 2008 #3

    dextercioby

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    Did you figure out how [itex] (1/2,0) \otimes (0,1/2) =(1/2,1/2) [/itex] ?
     
  5. Jan 21, 2008 #4
    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
     
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