I was reading about the Klein Gordon equation of scalar fields. I notice that the hamiltonian is not Hermitian: ∂0(Φ,π)T = matrix((0,1),(-p2,0)) (Φ,π)T The Hamiltonian operator iH = matrix((0,1),(-p2,0)) is not a hermitian matrix. What does this mean? Does this mean Klein Gordon fields don't conserve particle number, or that this is not Unitary? Is a quantum field theory with just Klein Gordon fields not valid?