Real Time Gluon Self-energy In A Background Field

The existence of quark-gluon plasma is predicted in finite-temperature lattice quantum chromodynamics(lattice QCD),and the exploration of quark-gluon plasma is an important part of high-energy nuclear physics.In the asymptotically free high temperature limit,we can calculate the relevant physical quantities using traditional perturbative QCD method.But in the semi-QGP region(Tc?4Tc),the non-perturbative physical effects cannot be ignored.Based on the simulation results of the phase transition order parameter Polyakov loop by lattice QCD,the value of the Polyakov loop in the semi-QGP region is between 0?1.The characteristics of this region can be described by introducing a non-zero background field.The main content of this paper is to calculate the one-loop self-energy of gluon in the background field.In the framework of real-time finite temperature field theory,three independent components of the gluon self-energy function under the Keldysh representation are obtained by using the hard thermal loops approximation,the three components are the delayed gluon energy function ?R,the advanced gluon energy function ?A and the symmetric gluon energy function ?F.We compare our results with the ones obtained without background field,and discuss the background field effects on gluon self-energy function.Using our results,the influence of the background field on the potential energy function of heavy quarks can be studied by the Dyson-Schwinger equations method,and it is expected to obtain the information of the binding energies and annihilation widths of heavy quarks even-elements on the background field.This will provide important information for the study of quarkonium depression in quark gluon plasma.After the introduction of the background field,the structure of the color space of the self-energy function is no longer a simple diagonal matrix,but with diagonal terms and off-diagonal terms.Among the diagonal term contributions of ?R and ?F,there is the contribution of the sum of distribution functions affected by the background field,na(k0)+nb(k0),which defined as the normal term.The contribution of the normal term of ?R is proportional to g2T2,and the contribution of the normal term of ?F is proportional to g2T3.But for the off-diagonal terms,there is also a contribution that depends on the difference na(ko)-nb(ko)of the distribution function,which is defined as anomalous term.Among them,the contribution of the anomalous term of ?R is proportional to g2T3,and there is an order of magnitude difference from the contribution of the normal term;The anomalous contribution of the ?F term is still proportional to g2T3.If we set the value of the background field to be zero,obviously the anomalous term is zero,and the corresponding normal term contribution return to the result obtained in the zero-background field.Our results show that for the normal contribution terms,the influence of the background field on the gluon energy function is only reflected in the correction of the Debye mass.Furthermore,we verify the Kubo-Martin-Schwinger relation.The results show that if we ignore the influence of anomalous contributions,the results after introducing the background field still satisfy the KMS condition.Previous studies have shown that the appearance of anomalous contributions will not be able to introduce a non-zero background field self-consistently through the equation of motion.To solve this problem,for ?R and ?A,we can eliminate the anomalous contribution by introducing two-dimensional gluon contribution.Useing the non-perturbative method to eliminate anomalous terms for ?F is the content we plan to do in the future.In addition,considering the background field,we also prove the KMS condition that generally exists between the three components of the gluon self-energy function.