- #1
Silviu
- 624
- 11
Hello! I am reading some notes on Lorentz group and at a point it is said that the irreducible representations (IR) of the proper orthochronous Lorentz group are labeled by 2 numbers (as it has rank 2). They describe the 4-vector representation ##D^{(\frac{1}{2},\frac{1}{2})}## and initially I thought this is an IR (also being a fundamental representation). However, further on they say that ##D^{(\frac{1}{2},\frac{1}{2})} = D^{(\frac{1}{2}, 0)} \oplus D^{(0,\frac{1}{2})}##, which implies that ##D^{(\frac{1}{2},\frac{1}{2})}## is not an IR. So I am confused, is it or is it not IR? The way I was thinking about it, is that the 4 dimensional vector representation (i.e. under Lorentz group) is an IR while the 4 dim spinor representation (i.e. under ##SL(2,C)##) is not IR. But wouldn't you need different notations for them? Then, ##D^{(0,\frac{3}{2})}## and ##D^{(\frac{3}{2},0)}## are also 4 dimensional, so what should I do with them? Are they IR, too? Can someone clarify this for me? Thank you!