In this work, a many body relativistic quantum field theory for the collective modes of spinor quantum electrodynamic theory (QED) plasmas is developed. We introduce the thermo field dynamics into the QED plasma study. The nontrivial background field method is used to take account of the non-perturbativity of background charged plasma particles and radiation field. It is an extension of "Furry picture" which is first introduced by Yuan Shi, et al. [Phys. Rev. A 94, 012124 (2016)] in their scalar QED plasma study. However, their wave function method in evaluating the background field of ideal system is hard to extend to the general many body cases. We propose a classical limit method that most perturbative high energy and quantum many body aspects can be included in a practical way. As an example, the wave propagation in unmagnetized electron-positron plasma is discussed. In the low energy limit case, the well known wave dispersion relations for non-relativistic degenerate plasma are recovered. In addition, mass increase of plasma particles due to the relativity, effective charge decrease due to the vacuum polarization, finite light velocity influence on the dispersion relation, and temperature influence on plasma system are discussed. Besides, new phenomenons including the zero sound of the electron-positron pair plasma and the particle production induced by the plasma oscillation are first reported. At last, the high energy limit case is studied.

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非磁化自旋 QED 等离子体中波传播的热场动力学背景场方法

在这项工作中，开发了用于自旋量子电动力学理论 (QED) 等离子体集体模式的多体相对论量子场理论。我们将热场动力学引入 QED 等离子体研究。非平凡背景场法用于考虑背景带电等离子体粒子和辐射场的非微扰性。它是袁世等人首先介绍的“毛茸茸的图片”的延伸。[物理。Rev. A 94, 012124 (2016)] 在他们的标量 QED 等离子体研究中。然而，他们的波函数方法评价理想系统的背景场很难推广到一般的多体情况。我们提出了一种经典的极限方法，可以以一种实用的方式包含大多数微扰高能和量子多体方面。举个例子，讨论了波在未磁化的正负电子等离子体中的传播。在低能量极限情况下，非相对论简并等离子体众所周知的波色散关系被恢复。此外，还讨论了由于相对性引起的等离子体粒子质量增加、真空极化引起的有效电荷减少、有限光速对色散关系的影响以及温度对等离子体系统的影响。此外，首次报道了正负电子对等离子体的零声波和等离子体振荡引起的粒子产生等新现象。最后，研究了高能量极限情况。讨论了相对性引起的等离子体粒子质量增加、真空极化引起的有效电荷减少、有限光速对色散关系的影响以及温度对等离子体系统的影响。此外，首次报道了正负电子对等离子体的零声波和等离子体振荡引起的粒子产生等新现象。最后，研究了高能量极限情况。讨论了相对性引起的等离子体粒子质量增加、真空极化引起的有效电荷减少、有限光速对色散关系的影响以及温度对等离子体系统的影响。此外，首次报道了正负电子对等离子体的零声波和等离子体振荡引起的粒子产生等新现象。最后，研究了高能量极限情况。