标题： 场论在边界存在情况下的量子化 显示英文标题

标题： Quantization of Field Theories in the Presence of Boundaries

摘要： 本文回顾了过去五年中在研究关于四维黎曼背景下的量子场的边界条件和半经典性质方面取得的进展。 对于无质量自旋-${1\over 2}$场，可以选择谱或超对称边界条件，相应的共形异常已通过zeta函数正则化方法进行了计算。 对于真空中的欧几里得麦克斯韦理论，已对BRST协变的法捷耶夫-波波夫振幅进行了逐模分析，适用于相对论性和非相对论性规范条件。 对于无质量自旋-${3\over 2}$场，已得到物理自由度对一环振幅的贡献，以及狄拉克和拉蒂塔-施温格势的二自旋子分析。 在线性化引力中，已详细研究了德唐德规范中的规范模和鬼模。 这一计划可能会加深对规范场和引力不同量化技术的理解，带来对规范不变性的新视角，并为扭量理论提供新的观点。 显示英文摘要

摘要： This paper reviews the progress made over the last five years in studying boundary conditions and semiclassical properties of quantum fields about 4-real-dimensional Riemannian backgrounds. For massless spin-${1\over 2}$ fields one has a choice of spectral or supersymmetric boundary conditions, and the corresponding conformal anomalies have been evaluated by using zeta-function regularization. For Euclidean Maxwell theory in vacuum, the mode-by-mode analysis of BRST-covariant Faddeev-Popov amplitudes has been performed for relativistic and non-relativistic gauge conditions. For massless spin-${3\over 2}$ fields, the contribution of physical degrees of freedom to one-loop amplitudes, and the 2-spinor analysis of Dirac and Rarita-Schwinger potentials, have been obtained. In linearized gravity, gauge modes and ghost modes in the de Donder gauge have been studied in detail. This program may lead to a deeper understanding of different quantization techniques for gauge fields and gravitation, to a new vision of gauge invariance, and to new points of view in twistor theory.