- #1
russel
- 13
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Hello there! Above is a problem that has to do with Lie Theory. Here it is:
The operators [itex]P_{i},J,T (i,j=1,2)[/itex] satisfy the following permutation relations:
[itex][J,P_{i}]= \epsilon_{ij}P_{ij},[P_{i},P_{j}]= \epsilon_{ij}T, [J,T]=[P_{i},T]=0[/itex]
Show that these operators generate a Lie algebra. Is that algebra a semisimple one? Also show that
[itex]e^{uJ}P_{i}e^{-uJ}=P_{i} \cos{u}+ \epsilon_{ij}P_{j} \sin{u}[/itex]
Does anyone know how to deal with it?
The operators [itex]P_{i},J,T (i,j=1,2)[/itex] satisfy the following permutation relations:
[itex][J,P_{i}]= \epsilon_{ij}P_{ij},[P_{i},P_{j}]= \epsilon_{ij}T, [J,T]=[P_{i},T]=0[/itex]
Show that these operators generate a Lie algebra. Is that algebra a semisimple one? Also show that
[itex]e^{uJ}P_{i}e^{-uJ}=P_{i} \cos{u}+ \epsilon_{ij}P_{j} \sin{u}[/itex]
Does anyone know how to deal with it?
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