标题： 绝热真空态由线性复结构导出 显示英文标题

标题： Adiabatic vacua from linear complex structures

摘要： 绝热真空中在宇宙时空中的量子场中起着核心作用，它们既作为特殊的初始条件，又是可观测量重整化的参考态。 本文引入了基于线性复结构的新方法，为确定绝热真空提供了一种有力的工具。 这些新方法推广了标准的WKB方法和刘易斯-赖森费尔德不变量，并允许我们研究具有广义二次时间依赖哈密顿量的多个耦合玻色自由度的问题。 我们证明了绝热数算符和有限阶的绝热真空可以表示为相同阶数的绝热复结构。 我们将我们的结果与仅适用于单一自由度的标准技术进行比较，并讨论其在宇宙时空中量子场、多体系统以及哈密顿量随参数缓慢变化的时间相关量子热力学问题中的适用性。 显示英文摘要

摘要： Adiabatic vacua play a central role in quantum fields in cosmological spacetimes, where they serve as distinguished initial conditions and as reference states for the renormalization of observables. In this paper we introduce new methods based on linear complex structures which provide a powerful tool for determining adiabatic vacua. The new methods generalize both the standard WKB appoach and the Lewis-Riesenfeld invariants, and allow us to study the problem of many coupled bosonic degrees of freedom with general quadratic time-dependent Hamiltonian. We show that the adiabatic number operator and the adiabatic vacuum of finite order can be expressed in terms of the adiabatic complex structure of the same order. We compare our results to standard techniques which apply only to a single degree of freedom, and comment on its applicability to problems in quantum fields in cosmological spacetimes, many-body systems and quantum thermodynamics, where the Hamiltonian is time dependent with slowly-changing parameters.