When the above hold, quantum theory can be extended to a Euclidean theory, defined by translating all the operators to imaginary time using the Hamiltonian. The commutation relations of the Hamiltonian, and the Lorentz generators, guarantee that Lorentz invariance implies rotational invariance, so that any state can be rotated by 180 degrees.
when the above hold quantum theory can be extended to a euclidean theory defined by translating all the operators to imaginary time using the hamiltonian the commutation relations of the hamiltonian and the lorentz generators guarantee that lorentz invariance implies rotational invariance so that any state can be rotated by 180 degrees