Undergrad Annihilation/creation operator question

[KevinMcHugh]

TL;DR

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?

 

[DarMM]

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.

 

[KevinMcHugh]

Thank you DarMM. I was under the assumption operators represent observables in QM.

 

[DarMM]

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.