标题： 量子场论中的渐近热核 显示英文标题

标题： Asymptotic Heat Kernels in Quantum Field Theory

摘要： 渐近展开首次由亨利·庞加莱于1886年引入。 本文描述了它们在具有边界的量子场论中振幅的半经典评估中的应用。 通过使用zeta函数正则化，在施加局部超对称边界条件的情况下，获得了平坦欧几里得背景中有边界的无质量自旋-${1\over 2}$场的共形异常。 然后通过关注高自旋场的共形异常，介绍了在存在边界的情况下规范场和引力的量化程序。 描述了协变Schwinger-DeWitt方法和非协变的逐模分析在何种条件下对量子振幅达成一致。 显示英文摘要

摘要： Asymptotic expansions were first introduced by Henri Poincare in 1886. This paper describes their application to the semi-classical evaluation of amplitudes in quantum field theory with boundaries. By using zeta-function regularization, the conformal anomaly for a massless spin-${1\over 2}$ field in flat Euclidean backgrounds with boundary is obtained on imposing locally supersymmetric boundary conditions. The quantization program for gauge fields and gravitation in the presence of boundaries is then introduced by focusing on conformal anomalies for higher-spin fields. The conditions under which the covariant Schwinger-DeWitt and the non-covariant, mode-by-mode analysis of quantum amplitudes agree are described.