Annihilation/creation operator question

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But in quantum field theory, the observables are found by integrating the Hamiltonian over spacetime, not by applying operators.In summary, these operators increase/decrease occupation number by one particle. They do not represent physical processes or observables, but are useful in quantum field theory. Only self-adjoint operators are considered observables in QM, but in QFT, observables are found by integrating the Hamiltonian over spacetime, not by applying operators.
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These operators increase/decrease occupation number by one particle. What observable do these operators represent?
I'm just curious what physical processes these operators represent. Since particles are created/destroyed in pairs, do they have to applied twice to describe an actual process?
 
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KevinMcHugh said:
Summary: These operators increase/decrease occupation number by one particle. What observable do these operators represent?

I'm just curious what physical processes these operators represent. Since particles are created/destroyed in pairs, do they have to applied twice to describe an actual process?
They don't represent physical processes or observables (they're not self adjoint or unitary). They're just formal operators useful in quantum field theory.

Wigner managed to find a way to classify all particle states in Minkowski spacetime. With each type there is an associated creation/annihilation operator and free quantum fields ultimately turn out to be just (generalized) Fourier transforms of them.
 
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Thank you DarMM. I was under the assumption operators represent observables in QM.
 
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KevinMcHugh said:
Thank you DarMM. I was under the assumption operators represent observables in QM.
Only self-adjoint operators do. And even then there are questions over whether all do.
 
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