Abstract
The polarisation tensor for the non-relativistic charged Bose gas in a uniform magnetic field is derived by using a gauge-independent second-quantised Hamiltonian approach in the random phase or one loop approximation. We utilise the tensor′s gauge invariant and symmetric properties to develop expressions for the dielectric tensor, the longitudinal dielectric response function, and the transverse dielectric response functions corresponding to photon propagation perpendicular and parallel to the magnetic field, so that detailed examinations of both the longitudinal and transverse properties of the system at T = 0 K and at finite temperatures may follow.
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