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.