标题： 协变相空间形式主义用于波动边界 显示英文标题

标题： Covariant Phase Space Formalism for Fluctuating Boundaries

摘要： 我们重新考虑了在具有边界的空间时间内制定$D$维规范理论的问题，重点放在引力理论的情形上。 我们将协变相空间形式化扩展到允许边界波动的情况。 我们分析了此情况下的辛形式、自由度（歧义）及其守恒性。 我们表明边界波动使所有表面电荷都可积。 我们研究了电荷的代数及其中心扩展、电荷守恒和通量。 我们简要评论了波动边界设定下记忆效应以及黑洞的半经典方面相关问题。 显示英文摘要

摘要： We reconsider formulating $D$ dimensional gauge theories, with the focus on the case of gravity theories, in spacetimes with boundaries. We extend covariant phase space formalism to the cases in which boundaries are allowed to fluctuate. We analyze the symplectic form, the freedoms (ambiguities), and its conservation for this case. We show that boundary fluctuations render all the surface charges integrable. We study the algebra of charges and its central extensions, charge conservation, and fluxes. We briefly comment on memory effects and questions regarding semiclassical aspects of black holes in the fluctuating boundary setup.