论文标题
无质量QCD和痕量异常的热力学压力
Thermodynamic pressure for massless QCD and the trace anomaly
论文作者
论文摘要
从统计力学中，任何能量量张量的热平均值的痕迹为$ \ langle t^μ_ {\; \; \;μ} \ rangle = t \ t \ partial p/\ partial p/\ partial p/\ partial partial t-4p $。重新归一化的组公式$ \ langle t^μ_ {\; \ \;μ} \ rangle =β（g_ {m}）\ partial p/p/partial p/\ p/\ p/\ partial g_ {m \ partial partial partial partial a partial paintial a partial for s s equ fermions at equ \ equ ferte the equath p = t^{4} \ sum_ {n = 0}^{\ infty} ϕ_ {n}（g_ {m}）\ big [\ ln \ big（{m \ over4πt} \ big）\ big）\ big]可以使用递归关系$ n \，ϕ__ {n}（g_ {n}（g_ {m}）（g_ {m}）= - ev（g_ {m}）= - （g_ {m}）$ n n $ n \ ge 1 $的功能，可以从$ n \ ge 1 $ for $ n \ ge 1 $计算出$ N \ ge 1 $。通过使用$（g_ {m}）^{2}的术语，（g_ {m}）^{3} $，$（g_ {m}）^{4} $ in $ nation_ {g_ {m}） （g_ {m}）^{5} $，$（g_ {m}）^{6} $ in $ ϕ_ {1}（g_ {m}）$和已知的顺序$（g_ {m}）^{6} $ in $（g_ {m}）上述系列可以求和，并给出与选择$ m =4πt$，即相同的结果。 $ t^{4} ϕ_ {0}（g_ {4πt}）$。
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. $T^{4}ϕ_{0}(g_{4πT})$.
