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arXiv 2207.00534hep-phhep-latnucl-th
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热场理论及其若干应用导论

An introduction to Thermal Field Theory and Some of its Application

Munshi G. Mustafa

AI总结:

本文系统介绍虚时热场理论,推导玻色子与费米子格林函数及配分函数,并在硬热圈近似下计算QED与QCD两点函数、自由能、压强及双轻子产生率。

摘要:

本文详细讨论了虚时形式下的热场理论。通过算符方法和泛函积分方法引入了虚时形式。讨论了玻色子和费米子频率求和的规则。推导了闵可夫斯基时间和欧几里得时间中的格林函数。计算了$ϕ^4$理论中的蝌蚪图和$ϕ^3$理论中的自能。讨论了存在热浴时费米子和玻色子一般两点函数的基本特征。然后得到了标量场、费米子场、规范场的自由配分函数以及相互作用标量场的配分函数。详细讨论了量子电动力学(QED)和规范固定。在硬热圈(HTL)近似下得到了QED中电子和光子的单圈自能。给出了热介质中电子和光子的色散性质和集体激发。得到了费米子和规范玻色子传播子的谱表示。在HTL近似下,概述了将QED两点函数结果推广到量子色动力学(QCD)的方法,其中主要涉及群论因子。作为有效场论方法,引入了HTL重求和和HTL微扰理论。在HTLpt框架内计算了重离子碰撞中产生的退禁闭QCD介质的前阶、次前阶和次次前阶自由能与压强。还概述了退禁闭QCD介质的一般特征,包括胶子凝聚和Gribov-Zwanziger作用量等非微扰效应。计算了具有这些非微扰效应的夸克-胶子等离子体的双轻子产生率。

英文摘要:

In this article an introduction to the thermal field theory within imaginary time has been discussed in details. The imaginary time formalism has been introduced through both the operatorial and the functional integration method. The prescription to perform frequency sum for boson and fermion has been discussed. Green's function both in Minkowski time as well as in Euclidean time has been derived. The tadpole diagram in $ϕ^4$ theory and the self-energy in $ϕ^3$ theory have been computed. The basic features of general two point functions for both fermions and bosons in presence of a heat bath have been discussed. Then the free partition functions for scalar, fermion and gauge field, and interacting scalar field have been obtained. The quantum electrodynamics (QED) and gauge fixing have been discussed in details. The one-loop self-energy for electron and photon in QED have been obtained in hard thermal loop (HTL) approximation. The dispersion properties and collective excitations of both electron and photon in a thermal medium have been presented. The spectral representation of fermion and gauge boson propagators have been obtained. In HTL approximation, the generalisation of QED results of two point functions to quantum chromodynamics (QCD) have been outlined that mostly involve group theoretical factors. As an effective field theory approach the HTL resummation and the HTL perturbation theory have been introduced. The leading order, next-to-leading order and next-to-next-leading order free energy and pressure for deconfined QCD medium created in heavy-ion collisions have been computed within HTLpt. The general features of the deconfined QCD medium have also been outlined with non-perturbative effects like gluon condensate and Gribov-Zwanziger action. The dilepton production rates from quark-gluon plasma with these non-perturbative effects have been computed.

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