- #1
filip97
- 31
- 0
Let we have ##J_i \in{J_1,J_2,J_3}## ,and ##K_i \in{K_1,K_2,K_3}##, rotation and boost generators respectable .
##A_i=\cfrac{1}{2}(J_i+iK_i)##, and
##[A_i,A_j]=i\epsilon_{ijk}A_k##
##[K_i,K_j]=-i\epsilon_{ijk}J_k##
##[J_i,K_j]=-i\epsilon_{ijk}K_k##
How proof that ##(m,n)A_i=J^{(m)}_i\otimes I_n## ?
I was proof that ##(m,n)(J_i+iK_i)=J^{(m)}_i\otimes I_n +I_m\otimes J^{(n)}_i \neq J^{(m)}_i\otimes I_n##
by definition that ## (m,n)(J_i,K_i)=J^{(m)}_i\otimes I_n + I_m\otimes K^{(n)}_i##
I was read Weinberg QFT Foundations , page 253 .
##A_i=\cfrac{1}{2}(J_i+iK_i)##, and
##[A_i,A_j]=i\epsilon_{ijk}A_k##
##[K_i,K_j]=-i\epsilon_{ijk}J_k##
##[J_i,K_j]=-i\epsilon_{ijk}K_k##
How proof that ##(m,n)A_i=J^{(m)}_i\otimes I_n## ?
I was proof that ##(m,n)(J_i+iK_i)=J^{(m)}_i\otimes I_n +I_m\otimes J^{(n)}_i \neq J^{(m)}_i\otimes I_n##
by definition that ## (m,n)(J_i,K_i)=J^{(m)}_i\otimes I_n + I_m\otimes K^{(n)}_i##
I was read Weinberg QFT Foundations , page 253 .