Covariant form of Trubnikov's response tensor for a relativistic magnetized thermal plasma

Abstract

A covariant version of Vlasov theory is used to derive the linear response 4-tensor for a relativistic magnetized thermal plasma, generalizing Trubnikov's 3-tensor form. The charge-continuity and gauge-invariance conditions imply a set of integral identities, and use of these identities allows one to derive a manifestly gauge invariant form for the response 4-tensor. This form implies an alternative version of Trubnikov's 3-tensor. The different versions lead to different expressions in the weakly relativistic small-gyroradius limit. Arguments are given as to how this inconsistency should be resolved.