When you rewrite the angular momentum generators J(adsbygoogle = window.adsbygoogle || []).push({}); _{i}and boost generators K_{j}in terms of the linear combinations N^{±}_{i}=J_{i}±iK_{i}, does this mean that your group parameters can now be complex? So for example a group element R can be written as:

[tex]R(z_1,z_2)=\exp[i(z_1 N^+ +z_2 N^-)] [/tex]

where the z's are complex? z1 and z2 must be complex conjugates in order to get something of the form:

[tex]R(z_1,z_2)=R(x,y)=\exp[i(xJ+yK)] [/tex]

where x and y are real group parameters instead of complex ones.

So is there an implicit rule that whatever the coefficient of N^{+}, the coefficient of N^{-}must be the complex conjugate? So in order to specify a group element of SO(4), you have to give 3 complex numbers (one for i=1,2,3), and the coefficients in front of the N^{-}generators would just be the complex conjugate of those numbers?

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# Lorentz algebra SO(4)

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