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.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?
Only self-adjoint operators do. And even then there are questions over whether all do.KevinMcHugh said:Thank you DarMM. I was under the assumption operators represent observables in QM.
The annihilation operator, denoted by a, is used to remove a particle from a quantum system. The creation operator, denoted by a†, is used to add a particle to a quantum system. They are essentially inverse operations.
The annihilation and creation operators are related by the commutation relation [a, a†] = 1, which means that they do not commute and their order matters. This relation is a fundamental property of quantum systems.
The commutation relation for annihilation and creation operators is important because it allows us to define the number operator, N = a†a, which counts the number of particles in a quantum system. This operator is used to describe many important physical phenomena, such as quantum states and energy levels.
In quantum field theory, annihilation and creation operators are used to describe the creation and annihilation of particles in a quantum field. They are used to construct field operators, which are used to describe the dynamics of particles and interactions between them.
Yes, annihilation and creation operators can be used to describe any type of particle, including bosons and fermions. However, the specific form of the operators may differ depending on the type of particle being described. For example, the operators for fermions must satisfy different commutation relations than those for bosons.