Abstract

We have developed the Hamiltonian theory for collective longitudinally polarized colorless excitations (plasmons) in a high-temperature gluon plasma using the general formalism for constructing the wave theory in nonlinear media with dispersion, which was developed by V.E. Zakharov. In this approach, we have explicitly obtained a special canonical transformation that makes it possible to simplify the Hamiltonian of interaction of soft gluon excitations and, hence, to derive a new effective Hamiltonian. The approach developed here is used for constructing a Boltzmann-type kinetic equation describing elastic scattering of collective longitudinally polarized excitations in a gluon plasma as well as the effect of the so-called nonlinear Landau damping. We have performed detailed comparison of the effective amplitude of the plasmon–plasmon interaction, which is determined using the classical Hamilton theory, with the corresponding matrix element calculated in the framework of high-temperature quantum chromodynamics; this has enabled us to determine applicability limits for the purely classical approach described in this study.

中文翻译：

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具有非阿贝尔相互作用的血浆中玻色激发的哈密顿形式主义

摘要

我们使用VE Zakharov开发的通用形式主义，在具有色散的非线性介质中构造波动理论，发展了一种高温胶子等离子体中的集体纵向极化无色激发（等离子体激元）的哈密顿理论。在这种方法中，我们明确获得了一种特殊的规范变换，从而可以简化软胶子激发相互作用的哈密顿量，从而得出一个新的有效哈密顿量。此处开发的方法用于构建玻尔兹曼型动力学方程，该方程描述胶子等离子体中集体纵向极化激发的弹性散射以及所谓的非线性Landau阻尼的影响。我们已经对等离激元-等离激元相互作用的有效幅度进行了详细的比较，使用经典汉密尔顿理论确定，并在高温量子色动力学框架内计算相应的矩阵元素；这使我们能够确定本研究中描述的纯经典方法的适用范围。