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Studying Quantum Magnets Using Ineracting Spin Wave TheoryA magnon is a quantized magnetic excitation hosted in a condensed matter state caused by deviations of the electron spin. Quantum fluctuations of the magnetic wave results in a quantized spin wave. Using spin wave theory we present a derivation of the interaction that describes magnons in a 3D ferromagnetic crystal lattice and a 2D antiferromagnetic crystal. We use both the Holstein-Primakoff and Dyson-Maleev bosonization transformation scheme. As in the literature, we find higher order interaction terms within the Hamiltonian. We present a derivation of these interaction terms and subsequent representation from a Feynman diagram approach.