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## Main Question or Discussion Point

I was reading about the Klein Gordon equation of scalar fields. I notice that the hamiltonian is not Hermitian:

∂

The Hamiltonian operator iH = matrix((0,1),(-p

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?

∂

_{0}(Φ,π)^{T}= matrix((0,1),(-p^{2},0)) (Φ,π)^{T}The Hamiltonian operator iH = matrix((0,1),(-p

^{2},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?