Creation and annihilation operators of Second qantization

                                    The creation and annihilation operators are the way to connect the first and second quantizations. It is fundamental for the many-body theory that every operator can be expressed in terms of annihilation and creation operators. Originally constructed in the context of the quantum harmonic oscillator, these operators are the most general form to describe quantum fields. Depending on the nature of the fields we can use two different approaches: