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The paper studies resonant generation of higher-order harmonics in a closedcavity in Euler-Heisenberg electrodynamics from the point of view of purequantum field theory. We consider quantum states of the electromagnetic fieldin a rectangular cavity with conducting boundary conditions, and calculate thecross-section for the merging of three quanta of cavity modes into a single one($3 \to 1$ process) as well as the scattering of two cavity mode quanta ($2 \to2$ process). We show that the amplitude of the merging process vanishes for acavity with an arbitrary aspect ratio, and provide an explanation based onplane wave decomposition for cavity modes. Contrary, the scattering amplitudeis nonzero for specific cavity aspect ratio. This $2 \to 2$ scattering is acrucial elementary process for the generation of a quantum of a high-orderharmonics with frequency $2\omega_1 - \omega_2$ in an interaction of twocoherent states of cavity modes with frequencies $\omega_1$ and $\omega_2$. Forthis process we calculate the mean number of quanta in the final state in amodel with dissipation, which supports the previous result of resonanthigher-order harmonics generation in an effective field theory approach.

Resonant generation of electromagnetic modes in nonlinear electrodynamics: Quantum perturbative approach