By Donald Melrose
The box of quantum plasmas has a protracted and various culture and is turning into of accelerating present curiosity, stimulated through purposes to micro-electronics and to centred high-power lasers. during this ebook, plasma kinetic conception is built a covariant (4-tensor) notation, which allows generalizations to incorporate all relativistic and electromagnetic results. Relativistic quantum results are integrated via synthesizing the idea with quantum electrodynamics (QED), together with the plasma responses in QED, and utilizing QED to calculate the plasma reaction 4-tensors.
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Additional resources for Quantum plasmadynamics: unmagnetized plasmas
Alternatively, one could choose to include only the longitudinal part of the response in P , by requiring P ∝ k, with the transverse part of the response included in M . 2) does not uniquely deﬁne how one is to separate into P and M for the non-static response. 15) in terms of Π µν (k) by writing χµνρσ (k) = µ0 µ ρ νσ k k Π (k) − k ν k ρ Π µσ (k) − k µ k σ Π νρ (k) + k ν k σ Π µρ (k) . 16) 28 1 Response 4-tensors This construction includes an implicit prescription of how the separation into P and M is made (speciﬁcally, M = 0).
Sometimes a dyadic notation is used to write the 3-tensors. The mixed component, Li j (k, u ˜), T i j (k, u ˜) become the ij components of the dyadics κκ, 1 − κκ, respectively, where κ = k/|k| is a unit vector along the wave vector. 14) and the additional identities Lµ µ (k, u) = k2 , (ku)2 T µ µ (k, u) = 2, Rµ µ (k, u) = 0. 15) It follows that one has Π L (k) = (k˜ u)4 Lµν (k, u ˜) Π µν (k), k4 Π T (k) = 12 Tµν (k, u ˜) Π µν (k), ˜) Π µν (k). 16) The component Π R (k) is nonzero only for systems that are optically active, and hence have a speciﬁc handedness.
1) in the propagator. There is no unique form for Dµν (k). The charge-continuity relation allows the addition of an arbitrary function times k ν to Dµν (k) without aﬀecting the value of Aµ (k). Also, Aµ (k) is deﬁned only to within a gauge transformation, and in a gauge-independent theory one may add an arbitrary function times k µ to Dµν (k), as this only causes a gauge transformation of Aµ (k). 5) where ξ(k) and ζ(k) are arbitrary. 4 Formal construction of the propagator One could deﬁne the Green’s function or photon propagator as a solution of Λµ ν (k)Dνρ (k) = µ0 g µρ .