标题： 旋量场在有边界流形中的世界线方法 显示英文标题

标题： Worldline approach for spinor fields in manifolds with boundaries

摘要： 世界线形式是量子场论中有用的方案，也已成为数值计算的强大工具。 它基于辅助点粒子的第一量化，其跃迁振幅对应于场论中量子涨落算子的热核。 然而，为了在有界流形上研究量子场论，需要将辅助点粒子的路径积分域限制为由这些边界所包围的特定世界线子集。 在本文中，展示了如何在二维弯曲半平面中的自旋场下，根据MIT袋边界条件实现这种限制，并计算前几个热核系数以验证所提出的构造。 此构造可以有几种推广。 显示英文摘要

摘要： 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 quantization of an auxiliary 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 auxiliary 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.