Since very early works on plasma oscillations in solids, it was known that in collective excitations (fluctuations of the charge density) of the electron gas there exists the resonance appearing as a quasiparticle of a special type called the plasmon. The elaboration of the quantum theory of plasmon in the framework of the canonical formalism is the purpose of the present work. the authors start from the establishment of the Lagrangian of the system of itinerant electrons in metal and the definition of the generalized coordinates and velocities of this system. Then the authors detennine the expression of the Hamiltonian and perform the quantization procedure in the canonical formalism. By means of this rigorous method the authors can derive the expressions of the Hamiltonians of the intemctions of plasmon with photon and all quasiparticles in solid from the first principles.
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