Momentum and Quasimomentum in the Physics of Condensed Matter
In the first part of these lectures the formulations of hydrodynamics by Euler and by Lagrange are laid out. Eulerian phonons carry momenta, in contrast to Lagrangian phonons, whose momenta are zero, but the momentum density of the fluid is the same. The proof is much shorter than in earlier papers.
The second, main, part starts from the familiar concept of the quasimomen-tum of phonons and electrons in solids and proceeds to quasimomentum (in contrast to ordinary momentum) in the classical theory of elasticity and electrodynamics of continuous media. Conservation of quasimomentum is proven for arbitrarily nonlinear and anisotropic homogeneous media; it even holds for dispersive media, whose energy depends on higher than the first derivatives of the fields. If the difference between the local (Eulerian) coordinates (used in electrodynamics) and the material (Lagrangian) coordinates (used in the theory of elasticity) is properly taken into account a new term in the expression for the quasimomentum of photoelastic media appears. Various applications of quasimomentum conservation are mentioned and a new kind of radioelectric effect is put forward.
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