Abstract
So far we have restricted our analysis to free bosonic and fermionic fields. In this case we were able to canonically quantize them, by associating with the fields and their conjugate momenta operators acting on a Hilbert space of states and satisfying the canonical commutation (or anti-commutation) relations and the equations of motion. This was possible since free fields can be represented as collections of infinitely many decoupled harmonic oscillators, each associated with a given one-particle state.
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