标题： 世界线方法对于流形上有边界的旋量场 显示英文标题

标题： Worldline approach for spinor fields in manifolds with boundaries

摘要： 世界线形式主义是量子场论中一种有用的方案，同时也成为数值计算的强大工具。 它基于点粒子的一阶量子化，其跃迁振幅对应于场论量子涨动算符的热核。 然而，为了研究束缚流形上的量子场论，需要将点粒子的路径积分域限制到由这些边界包围的世界线的一个特定子集上。 本文展示了如何针对二维弯曲半平面中满足MIT袋边界条件的旋量场实现这一限制，并计算前几个热核系数以验证所提出的构造。 该构造允许多种推广。 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 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.