- #1
kuecken
- 17
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I was wondering about the following
Λ=I+iT
T are the generators and Λ a continuous LT transformation, thus it is real. Therefore T needs to be imaginary.
And we can find two sets one being the generators for SO(3) J_i and the other for boosts K_i, which are both imaginary.
Now I am wondering about introducing the new basis of generators to make the Lie algebra look more like the one from angular momentum
J±=1/2(J_i±i*K_i)
How can this be a generator as it is complex and would make Λ complex therefore in the first expression?
What am I overlooking or misunderstanding here?
Thank you for your help.
Λ=I+iT
T are the generators and Λ a continuous LT transformation, thus it is real. Therefore T needs to be imaginary.
And we can find two sets one being the generators for SO(3) J_i and the other for boosts K_i, which are both imaginary.
Now I am wondering about introducing the new basis of generators to make the Lie algebra look more like the one from angular momentum
J±=1/2(J_i±i*K_i)
How can this be a generator as it is complex and would make Λ complex therefore in the first expression?
What am I overlooking or misunderstanding here?
Thank you for your help.