Covariant Calculations at Finite Temperature: The Relativistic Plasma
Covariant Calculations at Finite Temperature: The Relativistic Plasma
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DOI：
10.1103/physrevd.26.1394
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发表时间：
1982-09
影响因子：
5
通讯作者：
H. Weldon
中科院分区：
文献类型：
--
作者：
H. Weldon
结果表明，如果使用依赖温度的传播子的Minkowski空间形式，并且考虑热浴的四速度数学，场论中的有限温度计算在所有阶段都是明显的洛伦兹协变的。新的张量结构通常涉及${u}_{\ensureath{\mu}}$，但受到协变电流守恒的严重限制。计算了非阿贝尔规范理论真空极化张量的一个完整的高温(T确保数学m)展开式，其数量级为{g}^{2}，并分别显示了在有限温度下出现的频率和波数的依赖关系。“电”和“磁”性质的协变现象学被应用于集体等离子体效应，其特征是具有{N}_f}$费米子的等离子体频率${{\ensuremath{\omega}}_{p}}^{2}=\frac{({N}_{f}+2N){g}^{2}{T}^{2}}{6}$。“电场”场的纵向简正模只对$\ensuremath{\omega}g{\ensuremath{\omega}}_{p}$；和$\ensuremath{\omega}l{\ensuremath{\omega}}_{p}$存在，所有的“电场”场都被屏蔽。横向简正波是沿\~{}\fi{}}{E}\ifmmode\times\else\texttimes\fi{}\stackrel{\ifmmode的平面波，$\ensuremath{\omega}g{\ensuremath{\omega}}_{p}$；的横简正波对于$\ensuremath{\omega}l{\ensuremath{\omega}}_{p}$，除了静态($\EnsureMath{\omega}=0$)情况外，横向“电场”和“磁场”都被屏蔽。
It is shown that finite-temperature calculations in field theory are manifestly Lorentz covariant at all stages if the Minkowski-space form of the temperature-dependent propagators is used and if the four-velocity ${u}_{\ensuremath{\mu}}$ of the heat bath is taken into account. New tensor structures involving ${u}_{\ensuremath{\mu}}$ generally arise but are severely constrained by covariant current conservation. A complete high-temperature ($T\ensuremath{\gg}m$) expansion of the vacuum polarization tensor for non-Abelian gauge theories is computed to order ${g}^{2}$ and displays the separate dependence on frequency $\ensuremath{\omega}$ and wave number $k$ that occurs at finite temperature. A covariant phenomenology of "electric" and "magnetic" properties is applied to the collective plasma effects, characterized by a plasma frequency ${{\ensuremath{\omega}}_{p}}^{2}=\frac{({N}_{f}+2N){g}^{2}{T}^{2}}{6}$ for $\mathrm{SU}(N)$ with ${N}_{f}$ fermions. The longitudinal normal modes of the "electric" field exist only for $\ensuremath{\omega}g{\ensuremath{\omega}}_{p}$; for $\ensuremath{\omega}l{\ensuremath{\omega}}_{p}$ all "electric" fields are screened. The transverse normal modes are plane waves along $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{E}\ifmmode\times\else\texttimes\fi{}\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{B}$ for $\ensuremath{\omega}g{\ensuremath{\omega}}_{p}$; for $\ensuremath{\omega}l{\ensuremath{\omega}}_{p}$ both transverse "electric" and "magnetic" fields are shielded except for the static ($\ensuremath{\omega}=0$) case.