Chiral Kinetic Equation In Non-Abelian Gauge Field

In recent years,there have been various chiral/spin effects which attract broad interest in relativistic heavy ion collisions,such as the chiral magnetic effect-s(CME),the chiral vorticity vffect(CVE),the chiral separate effect(CSE)and the global polarization effect(GPE),which have opened up a new window to s-tudy hot and dense nuclear matter at quantum level.These chiral/spin effects are directly related to the vacuum structure of quantum chromodynamics(QCD)and the breaking of CP symmetry in nature,so it is very important to study these effects further.Relativistic heavy ion collision is a fast-evolving dynamic system.In order to quantitatively describe the CME,the CVE and the GPE,we must consider the dynamic evolution of these quantum effects.The quantum kinetic theory based on the Wigner function is a theoretical framework for describing quantum effects and non-equilibrium processes from the first principle of quantum field theory,and it is an ideal theoretical tool for self-consistently describing these chiral/spin effects.However,at present,most research on quantum kinetic theory is focused on the chiral kinetic theory(CKT)under Abelian gauge field,i.e.,electromagnet-ic field,the CKT under non-Abelian gauge field is rarely discussed.However,the dynamics of quark gluon plasma(QGP)in relativistic heavy ion collisions is mainly determined by non-Abelian gauge field.we known little about the effects of non-Abelian gauge fields on these chiral/spin effects.In addition,how deco-herence occurs from the classical non-Abelian color field to the QGP is still an open question.These important physical problems urge us to further develop the CKT under the non-Abelian field.This is the main research motivation and goal of this dissertation.In quantum transport theory based on the Wigner function,we can select the left-handed/right-handed vector part of the Wigner function as the basic component.Under the chiral limit,the left-handed/right-handed Wigner func-tions are decoupled from other scalar,pseudoscalar,tensor Wigner functions,and the left-handed and right-handed Wigner functions are also decoupled from each other,which greatly simplifies the quantum transport equation.With the help of semi-classical expansion,we can entangle the Wigner equations and de-rive the chiral kinetic equation under the SU(N)non-Abelian gauge field step by step.Firstly,similar to the Abelian field,we find that only one of the four space-time components of the left-handed/right-handed vector Wigner function is independent.The time-like component is selected as the basic particle phase space distribution function,and other space-like components can be derivative from the distribution function.Thus,four space-time components of the Wigner function have been reduced into only one.We find that some Wigner equa-tions give the on-shell conditions,and some are reduced to constraint equations.These constraint equations are the peculiar results of the non-Abelian gauge field distinguished from the Abelian case.Secondly,we further decompose the left-handed/right-handed Wigner function into a color singlet and N2-1 color octet.We give the Lorentz covariant forms of the singlet and octet chiral kinet-ic equations in the eight-dimensional phase space(four-dimensional momentum space and four-dimensional coordinate space).We find that even in the zero-order Wigner equation,these different color components are coupled with each other.This reflects the speciality and complexity of the non-Abelian field dis-tinguished from the Abelian field.Thirdly,the particle phase space distribution function in the classical transport theory is always the Lorentz scalar function,however the definition of the particle distribution function in the chiral transport theory depends on the reference system we observe,it is not a Lorentz scalar.So when we change the reference frame,the particle distribution function will change accordingly.In this paper,we give the non-trivial Lorentz transformation rules of the particle distribution function in different reference systems,and com-pared it with the Abelian case.Finally,we transform the particle distribution function and chiral kinetic equation of the eight-dimensional phase space into seven-dimensional(three-dimensional momentum space and four-dimensional co-ordinate space)forms by integrating the zero component of momentum.After integrating,we remove the singular delta function.Seven-dimensional transport equation can be the starting point for the future numerical simulation.In our present work,we did not have the chance to use the CKT to deal with some phenomenological calculation due to the time limit in the master's stage.In the upcoming doctoral period,based on this non-Abelian CKT,the author will discuss the non-Abeian chiral anomaly effect,the chiral chromo-magnetic effect,the chiral chromo-magnetic separation effect,and the effects of various chiral chromo-currents that can be induced by vortiticy.The numerical calculations will be carried out to quantitatively estimate the effects on the GPE and the CME,the CVE and the CSE influenced by non-Abelian field.