Wider Applications of Lattice Field Theory

量子场论是理论物理中最成功和最广泛使用的方法之一，然而，在某些情况下，数学方程不是用纸笔可以解的。一种可能的第一原理数值技术是格子场理论，在该理论中，空间和时间的连续维度被限制在固定的点网格上，这些点之间有联系。通过这种方式，可以使用计算机对系统进行建模，并随着网格上点数的增加而提高精度。这种方法已被广泛用于研究量子色动力学，这是一种支配夸克之间相互作用的强核力理论，由于相互作用的强度，该理论不能解析求解。晶格场理论也可以用来研究许多物体系统的行为，例如石墨烯，这在凝聚态物理中是相关的。格子场理论越来越多地被用于研究超越标准模型物理的行为，例如，包括超对称性的模型以及弦理论的矩阵模型，如Banks-Fischler-Shenker-Susskind模型。一个特别令人感兴趣的领域是量子混沌。经典地说，混沌是由最初接近的状态以指数速度彼此分离的路径定义的。这种行为也可以在量子系统中观察到，并在许多物体系统的热化过程中发挥关键作用，例如重离子碰撞产生的夸克-胶子等离子体。由于黑洞是最混沌的量子系统，对量子混沌的研究也可能有助于揭示量子引力理论。在这个项目中，我们计划研究多体量子系统中近乎最大的量子混沌的出现。这种处于最大混沌状态的系统将为我们提供类黑洞物理的微观模型。特别是，我们计划开发从欧几里德时间的蒙特卡罗模拟结果中提取热化率(最大Lyapunov指数)的方法。我们还计划用这些方法来研究强相互作用规范理论中Lyapunov指数的温度依赖性。除此之外，我们还将寻求将格子场理论应用于各种其他模型，包括我之前合作的继续工作，该工作使用格子场理论来证明手征对称破缺的开始和Gross-Witten-Wadia转变，在约束和部分约束之间，在江口-川井模型中重合。

Quantum field theory is one of the most successful, and widely used, approaches in theoretical physics however, in some cases the mathematical equations are not solvable using a pen and paper. One possible first-principle numerical technique is lattice field theory, in which the continuous dimensions of space and time are restricted to a fixed grid of points with links between them. In this way a system can be modelled using a computer, with increasing precision as the number of points on the grid is increased. This method has been widely used to investigate quantum chromodynamics, the theory of the strong nuclear force that governs the interactions between quarks, which is not analytically solvable due to the strength of the interactions. Lattice field theory may also be used to investigate the behaviour of many body systems, such as graphene, which is relevant in condensed matter physics. Increasingly lattice field theory is being used to investigate the behaviour of beyond the standard model physics, for example, models which include supersymmetry as well as matrix models of string theory such as the Banks-Fischler-Shenker-Susskind model. One area of particular interest is quantum chaos. Classically chaos is defined by the paths of initially close states separating from one another at an exponential rate. This behaviour can also be observed in quantum systems and plays a key role in the thermalization of many body systems, such as the quark-gluon plasma produced during collisions of heavy ions. With black holes being maximally chaotic quantum systems, studies of quantum chaos might also shed light on the theory of quantum gravity. In this project, we plan to study the emergence of nearly maximal quantum chaos in many-body quantum systems. Such systems in the regime of maximal chaos will provide us with microscopic models for black-hole-like physics. In particular, we plan to develop methods for the numerical extraction of thermalization rates (largest Lyapunov exponents) from the results of Monte-Carlo simulations in Euclidean time. We further plan to apply these methods to study the temperature dependence of Lyapunov exponents in gauge theories of strong interactions. In addition to this we will look to employ lattice field theory to a variety of other models, including continuing work that I collaborated on previously which used lattice field theory to demonstrate that the onset of chiral symmetry breaking and the Gross-Witten-Wadia transition, between confinement and partial confinement, coincide in the Eguchi-Kawai model.