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Heirot
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Let's say that we're trying to calculate J_z|0> for spinor field. Now, one would naturally expect that it vanishes as do all of the observables in vacuum state. On the other hand, J_z isn't diagonal in the number basis, so one has J_z|0> ~ |2>, i.e. particle + antiparticle state due to the two creation operators in J_z. So, which one is it? All the books I've seen says that it vanishes. But the direct calculations says it isn't so.
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