临界现象与泛函重整化群

Critical phenomena and functional renormalization group

本文主要介绍了近年来泛函重整化群(FunctionalRenormalizationGroup,f RG)在量子色动力学(Quantum Chromodynamics,QCD)相变及其临界现象研究中的一些进展,主要侧重于与QCD的临界终点(Critical End Point,CEP)相关的非微扰临界指数的计算、重子数的涨落等。fRG是一种非微扰连续场论的理论方法,其基本思想是通过重整化群能标从高能向低能的演化,连续不断地将不同尺度的量子涨落以及热涨落积分到理论体系当中。本文讨论了非微扰有效势重整化群流方程和不动点方程的各种求解方法,包括泰勒展开、空间维数ε=4-d展开以及最近被提出的非局域势直接求解方法。还系统地讨论了与QCD的临界终点等临界现象密切相关的重子数的涨落,探讨了实验观测到的净质子数分布的峰度,也就是四阶矩随碰撞能量非单调依赖关系的可能原因。

Recent progress in studies on quantum chromodynamics(QCD)phase transition and related critical phenomena within the functional renormalization group(fRG)approach were reviewed,including the nonperturbative critical exponents and baryon number fluctuations,which are pertinent to the critical end point(CEP)in the QCD phase diagram.The fRG is a nonperturbative continuum field approach,in which quantum thermal fluctuations are successively integrated with the evolution of the renormalization group(RG)scale.Different methods of finding solutions to the flow or fixed-point equations of a nonperturbative effective potential have been discussed,for example,the Taylor expansion,expansion of the spatial dimensionε=4−d,and the recently proposed direct solution of the global potential.Furthermore,the baryon number of fluctuations is relevant to the critical phenomena of the CEP.Both have been discussed,and one explores the underlying reasons for the observed non-monotonic dependence of the kurtosis of the net proton number of distributions on collision energy in experiments.