- #1
Pietjuh
- 76
- 0
Hello, perhaps this is the most dumb question ever, but I don't see why it holds.
I'm looking at the irreducible representations of the Lie group U(1). To find them I considered the irreps of the lie algebra u(1). These irreps are obviously 1 dimensional and are given by f(a i ) = p a i for some real number p. If I now exponentiate this result I find that the irreducible representations of U(1) are given by g( exp(i theta) ) = exp(i p theta). But I read that p must be an integer. I cannot see however why this must be true! :(
Thanks in advance
I'm looking at the irreducible representations of the Lie group U(1). To find them I considered the irreps of the lie algebra u(1). These irreps are obviously 1 dimensional and are given by f(a i ) = p a i for some real number p. If I now exponentiate this result I find that the irreducible representations of U(1) are given by g( exp(i theta) ) = exp(i p theta). But I read that p must be an integer. I cannot see however why this must be true! :(
Thanks in advance