# Tag Info

## New answers tagged lie-algebra

### Showing that the angular momentum operators and Laplace-Runge-Lenz operator together are generators of $SO(4)$

This is not the math site. Just follow the strategy of wikipedia and, noting that H commutes with L and A, it can be moved out of their commutators just like a constant number. (In its diagonal ...
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### Writing gauge transformation of the gauge fields explicitly in terms of coordinates

Assume a field $\psi(x)$ transforming with respect to some arbitrary representation $$U(x)=e^{-i \alpha_a(x) T_a}, \qquad [T_a,T_b]= i f_{abc}T_c$$ of your gauge group. Defining the matrix-valued ...
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### Writing gauge transformation of the gauge fields explicitly in terms of coordinates

Your derivative term should be $$(\partial_\mu g) g^{-1}.$$ This combination is an element of the Lie algebra,and so expressible as a sum of the $t^\alpha$, unlike the group element $g$ itself. It'...
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