Time-reversal-invariant projection operators for lattice dynamics

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Abstract
An expression for a time-reversal-invariant projection operator which can be used to generate the columns of the unitary matrix which block diagonalizes the dynamical matrix of the lattice-dynamics problem in the harmonic approximation is given. The use of this operator and some of its properties is summarized. One interesting result is that the eigenvectors of the dynamical matrix can be expanded in terms of the columns of the unitary matrix which block diagonalizes the dynamical matrix and that the coefficients in the expansion are real numbers.

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