Annihilation operator
In physics, an annihilation operator is the operator in quantum field theory that lowers the number of particles in a given state by one.
Also, a creation operator is an operator that increases the number of particles in a given state by one, and it is the Hermitian conjugate of the annihilation operator.
The mathematics behind the creation and the annihilation operators is identical as the formulae for ladder operators that appear in the quantum harmonic oscillator. For example, the commutator of the annihilation and the creation operator associated with the same state equals one; all other commutators vanish.
While the concept of creation and annihilation operators is well defined for free field theories, in interacting QFTs, they can only be defined in the interaction picture, which does not exist according to Haag's theorem.
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