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Dyson-Schwinger variational approach to quantum field theory

量子场论的 Dyson-Schwinger 变分方法

基本信息

批准号：
275682849
负责人：
Professor Dr. Hugo Reinhardt
金额：
--
依托单位：
Institut für Theoretische Physik
依托单位国家：
德国
项目类别：
Research Grants
财政年份：
2015
资助国家：
德国
起止时间：
2014-12-31 至 2018-12-31
项目状态：
已结题

来源：
https://gepris.dfg.de/gepris/projekt/275682849?language=en
关键词：
Dyson Schwinger variational approach quantum

项目摘要

The goal of the intended research project is the development of a general non-perturbative Hamiltonian approach to quantum field theory in the continuum, which is based on a variational principle with non-Gaussian vacuum wave functionals. To this end, the wave functional is written as the exponent of an "action", which is expanded in powers of the fields. The non-local kernels (variational kernels) appearing as expansion coefficients will be determined by minimizing the vacuum energy density. The centerpiece of the approach are generalized Dyson-Schwinger equations (DSEs), which allow to express the n-point functions of the fields (and, in particular, the energy) by the variational kernels. This approach leads to a system of equations of motion, which contains, besides the generalized DSEs, also the gap equations for the variational kernels obtained by minimizing the energy. This system of integral equations has to be solved self-consistently. The approach is not restricted to relativistic quantum field theories, but is also well suited for a non-perturbative treatment of interacting many-body systems and allows a systematic improvement of the mean field approximation. Specifically, the approach shall be worked out for QCD in Coulomb gauge. For this purpose, a vacuum wave functional is used which contains in the exponent up to quartic terms in the gauge field, as well as the coupling of the quarks to the gluons. In a first step, the resulting equations of motions shall be solved analytically by power expansion in momentum space for the n-point functions in both the IR and the UV. Subsequently, these equations shall be solved numerically in the entire momentum region. This shall be done first in the so-called quenched approximation, and subsequently also in an unquenched calculation.

本研究计划的目标是在非高斯真空波泛函的变分原理的基础上，发展一种通用的非摄动哈密顿方法来研究连续介质中的量子场论。为此，波泛函被写成“作用”的指数，以场的幂展开。以膨胀系数形式出现的非局部核（变分核）将通过最小化真空能量密度来确定。该方法的核心是广义Dyson-Schwinger方程（DSEs），它允许通过变分核来表示场（特别是能量）的n点函数。这种方法导致了一个运动方程系统，它除了包含广义的DSEs外，还包含通过最小化能量得到的变分核的间隙方程。这个积分方程组必须自洽地求解。该方法不仅限于相对论量子场论，而且也非常适合于相互作用的多体系统的非摄动处理，并允许系统地改进平均场近似。具体来说，对于库仑量规的QCD，需要制定出相应的方法。为此，使用了一个真空波泛函，它在指数中包含了规范场中最高四次项，以及夸克与胶子的耦合。在第一步，得到的运动方程应在动量空间中对红外和紫外的n点函数进行幂展开式解析求解。随后，在整个动量区域内对这些方程进行数值求解。这应首先在所谓的淬火近似中进行，然后在非淬火计算中进行。