Uses in Quantum Field Theory
The vacuum expectation value of a normal ordered product of creation and annihilation operators is zero. This is because, denoting the vacuum state by, the creation and annihilation operators satisfy
(here and are creation and annihilation operators (either bosonic or fermionic)).
Any normal ordered operator therefore has a vacuum expectation value of zero. Although an operator may satisfy
we always have
This is particularly useful when defining a quantum mechanical Hamiltonian. If the Hamiltonian of a theory is in normal order then the ground state energy will be zero: .
Read more about this topic: Normal Order
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