Landau's problem in the noncommutative quantum mechanics and linearized gravitational waves: DeWitt's approach

Abstract

We present a systematic study of the noncommutative interaction of gravitational waves with matter at the quantum mechanical level in the long wavelength and small velocity limit. In particular, the noncommutative quantum dynamics of the Landau's problem is employed to measure the transmission amplitudes in terms of the Riemann's tensor elements by a gravitational wave in linearized approximation. It turns out that the Hamiltonian of the charged particles derived based on DeWitt's approach is valid by the deformed electromagnetic fields.