The Hamiltonian operator in normal form

Wick s theorem (3.109), which gives the prescription for handling products of creation and annihilation operators may, of course, be applied to the Hamiltonian operator, 5f, when it is expressed in the second-quantization formalism, eq. (3.91)  

This leads immediately to the Hamiltonian operator in a form which is of primary importance for perturbation treatments and many-body formalism. This form of the Hamiltonian operator is termed the normal product form. It is usually written as follows  

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