Suppose I can write my Hamiltonian as above. $J_x, J_y, J_z$ and $Q$, etc. are operators.
It is obvious that I can add the terms as I want: I can add $J_x + J_y + J_z + ...$ or $J_y + J_x + J_z ...$ or etc.
From my Hamiltonian, I can get a unitary operator. Since it is exponential, what I figured out is that I can use Lie-Trotter Product Formula,
But since $J_x$ and $J_y$ and $J_z$ do not commute, then the operators' sequence matter. So now my Hamiltonian gives different unitary operator as I add the operators differently.
I am confused because when viewing Hamiltonian, I can just add the operators I want, but when it comes to unitary operator, I cannot.
What is right?