近日，阿根廷国家科学技术研究委员会与拉普拉塔国立大学的Lucas Manzo及其研究团队取得一项新进展。经过不懈努力，他们提出具有边界流形中旋量场的世界线方法。相关研究成果已于2024年6月21日在国际知名学术期刊《高能物理杂志》上发表。

世界线形式论，作为量子场论中的一种高效方案，已成为数值计算的重要工具。它根植于点粒子的第一次量子化，其中跃迁振幅直接映射到场论量子涨落算子的热核。然而，当研究有界流形中的量子场论时，研究人员需对点粒子的路径积分域进行限制，使其仅限于由这些边界所围成的特定世界线子集。

本文给出了在MIT袋边界条件下二维弯曲半平面上的旋量场如何实现这一限制，并计算了前几个热核系数作为所提出构造的验证。这种构造可以作几种概括。

附：英文原文

Title: Worldline approach for spinor fields in manifolds with boundaries

Author: Manzo, Lucas

Issue&Volume: 2024-06-21

Abstract: The worldline formalism is a useful scheme in Quantum Field Theory which has also become a powerful tool for numerical computations. It is based on the first quantisation of a point-particle whose transition amplitudes correspond to the heat-kernel of the operator of quantum fluctuations of the field theory. However, to study a quantum field theory in a bounded manifold one needs to restrict the path integration domain of the point-particle to a specific subset of worldlines enclosed by those boundaries. In the present article it is shown how to implement this restriction for the case of a spinor field in a two-dimensional curved half-plane under MIT bag boundary conditions, and compute the first few heat-kernel coefficients as a verification of the proposed construction. This construction admits several generalisations.

DOI: 10.1007/JHEP06(2024)144

Source: https://link.springer.com/article/10.1007/JHEP06(2024)144