Pair Modes in Relativistic Quantum Plasmas

Pair modes were identified by Hines and collaborators as longitudinal waves in a relativistic quantum plasma of spin 0 particles in the completely degenerate limit. Pair modes with both longitudinal and transverse polarization also exist in spin 1 plasmas in the completely degenerate limit. We consider the possible existence of pair modes in completely degenerate, spin ½ plasmas, with a negative conclusion. It is argued that pair modes are associated with a pole (in the response function) that is present only in the presence of a Bose condensate. The properties of these wave modes, including their energetics, are discussed.