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arXiv 2209.09764hep-th
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无质量QCD和迹线anomaly的热力学压力

Thermodynamic pressure for massless QCD and the trace anomaly

H. Arthur Weldon

备注：
4 pages. Error corrected in Sec III.A now gives complete agreement with Ref [11]
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摘要：

从统计力学来看，任何能量动量张量的热平均迹都是$\langle T^μ_{\;\;μ}\rangle =T\partial P/\partial T-4P$。无质量费米子QCD的重整化群公式$\langle T^μ_{\;\;μ}\rangle =β(g_{M})\partial P/\partial g_{M}$要求压强具有结构\begin{equation} P=T^{4}\sum_{n=0}^{\infty} ϕ_{n}(g_{M})\big[\ln\big({M\over 4πT}\big)\big]^{n},\end{equation}，其中因子$4π$是为了后面的方便。可以使用递归关系$n\,ϕ_{n}(g_{M})=-β(g_{M})dϕ_{n-1}/dg_{M}$从$ϕ_{0}(g_{M})$计算用于$n\ge 1$的函数$ϕ_{n}(g_{M})$。通过使用$ϕ_{0}(g_{M})$中的阶数$(g_{M})^{2}, (g_{M})^{3}$、$(g_{M})^{4}$的项来对照已知的微扰理论结果进行检查，以获得$ϕ_{1}(g_{M})$中的阶数$(g_{M})^{4}, (g_{M})^{5}$、$(g_{M})^{6}$的已知项和$ϕ_{2}(g_{M})$中的阶数$(g_{M})^{6}$的已知项。上述系列可以求和，并给出与选择$M=4πT$相同的结果，即$T^{4}ϕ_{0}(g_{4πT})$。

英文摘要：

From statistical mechanics the trace of the thermal average of any energy-momentum tensor is $\langle T^μ_{\;\;μ}\rangle =T\partial P/\partial T-4P$. The renormalization group formula $\langle T^μ_{\;\;μ}\rangle =β(g_{M})\partial P/\partial g_{M}$ for QCD with massless fermions requires the pressure to have the structure \begin{equation} P=T^{4}\sum_{n=0}^{\infty} ϕ_{n}(g_{M})\big[\ln\big({M\over 4πT}\big)\big]^{n},\end{equation} where the factor $4π$ is for later convenience. The functions $ϕ_{n}(g_{M})$ for $n\ge 1$ may be calculated from $ϕ_{0}(g_{M})$ using the recursion relation $n\,ϕ_{n}(g_{M})=-β(g_{M})dϕ_{n-1}/dg_{M}$. This is checked against known perturbation theory results by using the terms of order $(g_{M})^{2}, (g_{M})^{3}$, $(g_{M})^{4}$ in $ϕ_{0}(g_{M})$ to obtain the known terms of order $(g_{M})^{4}, (g_{M})^{5}$, $(g_{M})^{6}$ in $ϕ_{1}(g_{M})$ and the known term of order $(g_{M})^{6}$ in $ϕ_{2}(g_{M})$. The above series may be summed and gives the same result as choosing $M=4πT$, viz. $T^{4}ϕ_{0}(g_{4πT})$.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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