论文标题
在弯曲空间中，蒙特卡洛的方法
A Monte Carlo Approach to the Worldline Formalism in Curved Space
论文作者
论文摘要
我们提出了一种数字方法，用于评估在弯曲的欧几里得空间上定义的世界线（WL）路径积分，并用蒙特卡洛（MC）技术采样。特别是，由于引入了二次术语，我们采用了一种称为Yloops的算法，并进行了轻微的修改，该术语具有稳定和加速收敛的功能。作为扰动对应物，我们的方法将动力学项与平面术语的非平凡度量和偏差视为相互作用项。此外，在当前WLMC中采用的数值离散化是在相关的骨点粒子的适当时间方面实现的，因此可以将这种过程视为已经引入了时间分段（TS）离散化的类似物，以在弯曲的空间中构建量子路径积分。结果，在计算过程中考虑了TS违反期限。该方法针对在D维最大对称空间中的自由骨点粒子的热内核的现有分析计算进行了测试。
We present a numerical method to evaluate worldline (WL) path integrals defined on a curved Euclidean space, sampled with Monte Carlo (MC) techniques. In particular, we adopt an algorithm known as YLOOPS with a slight modification due to the introduction of a quadratic term which has the function of stabilizing and speeding up the convergence. Our method, as the perturbative counterparts, treats the non-trivial measure and deviation of the kinetic term from flat, as interaction terms. Moreover, the numerical discretization adopted in the present WLMC is realized with respect to the proper time of the associated bosonic point-particle, hence such procedure may be seen as an analogue of the time-slicing (TS) discretization already introduced to construct quantum path integrals in curved space. As a result, a TS counter-term is taken into account during the computation. The method is tested against existing analytic calculations of the heat kernel for a free bosonic point-particle in a D-dimensional maximally symmetric space.
