Covariant response tensors for spin zero and spin one boson/anti-boson plasmas

A fully covariant and general expression for the relation between the 4-current and the 4-potential for spin 0 and spin 1 particle/anti-particle plasmas is presented. The response tensors obtained are compared with the spin 1/2 case, and are shown to reproduce the classical expressions in the appropriate limit. The longitudinal and transverse parts of the linear response tensor are evaluated for an isotropic particle/anti-particle distribution, and explicit expressions are obtained for the completely degenerate limit. The dispersion equations for longitudinal and transverse waves are derived for a completely degenerate plasma. Three transverse wave modes are found as the degenerate limit is approached; one mode is identified as the familiar transverse mode of any isotropic plasma, a second mode is an analogue of the 'pair branch' for longitudinal waves, and the third mode is referred to as the 'roton-like' mode due to the form of its dispersion relation