论文标题
避免晶格场理论中的标志问题
Avoiding the sign-problem in lattice field theory
论文作者
论文摘要
在晶格场理论中，可以通过高维积分来计算基本颗粒的相互作用。基于重要性采样的马尔可夫链蒙特卡洛（MCMC）方法通常有效地解决这些积分的大多数。但是这些方法给出了振荡性积分的巨大错误，显示出所谓的标志问题。我们使用考虑系统的对称性制定了新的正交规则，以避免在物理一维模型中为产生的高维积分中的符号问题。本文简要介绍了晶格QCD中使用的积分，其中研究了Gluon和Quark基本粒子的相互作用，并解释了我们开发的替代整合方法，并显示了将它们应用于具有一个物理维度的模型的结果。新的正交规则避免了符号问题，因此可以在直到现在的参数空间中进行模拟，其中MCMC错误对于负担得起的样本量太大。但是，对于使用物理高维系统的应用，进一步开发这些技术仍然是一个挑战。
In lattice field theory, the interactions of elementary particles can be computed via high-dimensional integrals. Markov-chain Monte Carlo (MCMC) methods based on importance sampling are normally efficient to solve most of these integrals. But these methods give large errors for oscillatory integrands, exhibiting the so-called sign-problem. We developed new quadrature rules using the symmetry of the considered systems to avoid the sign-problem in physical one-dimensional models for the resulting high-dimensional integrals. This article gives a short introduction to integrals used in lattice QCD where the interactions of gluon and quark elementary particles are investigated, explains the alternative integration methods we developed and shows results of applying them to models with one physical dimension. The new quadrature rules avoid the sign-problem and can therefore be used to perform simulations at until now not reachable regions in parameter space, where the MCMC errors are too big for affordable sample sizes. However, it is still a challenge to develop these techniques further for applications with physical higher-dimensional systems.
