The total isospin is defined as $$ \hat{T}=\sum_{i=1}^A\hat{\tau}_i, $$ and its corresponding isospin projection as $$ \hat{T}_z=\sum_{i=1}^A\hat{\tau}_{z_i}, $$ with eigenvalues \( T(T+1) \) for \( \hat{T} \) and \( 1/2(N-Z) \) for \( \hat{T}_z \), where \( N \) is the number of neutrons and \( Z \) the number of protons.

If charge is conserved, the Hamiltonian \( \hat{H} \) commutes with \( \hat{T}_z \) and all members of a given isospin multiplet (that is the same value of \( T \)) have the same energy and there is no \( T_z \) dependence and we say that \( \hat{H} \) is a scalar in isospin space.